... In particular, the short-range magnetic order at temperatures above the magnetic-transition p... more ... In particular, the short-range magnetic order at temperatures above the magnetic-transition point is not completely destroyed (in the two-dimensional case it is retained at temperatures up to T $jJ j), so that there exists a wide temperature range T > TM with a strong short-range ...
A generalized supersymmetric representation of the Hubbard operator algebra is considered. This r... more A generalized supersymmetric representation of the Hubbard operator algebra is considered. This representation is applied to the infinite-U Hubbard model. A mean-field theory which takes into account both on-site and inter-site virtual boson-fermion transitions is developed. Unlike previous approaches, the mean-field theory considered is free from divergences. Possible application of these results to the ferromagnet-paramagnet transition, as well as to other problems is discussed.
The problem of the symmetry of the superconducting pairing and the form of the gap function in th... more The problem of the symmetry of the superconducting pairing and the form of the gap function in the electron-doped superconductors is reconsidered within the temperature-cutoff functional renormalization group approach combined with the Bethe-Salpeter equations. The momentum dependence of the order parameter for antiferromagnetic and superconducting instabilities in these compounds is analyzed. The gap function in the antiferromagnetic (particle-hole) channel has its maxima at the hot-spots, or at the diagonal of the Brilloin zone in their absence. The wavefunction in the singlet superconducting channel is non-monotonic in the vicinity of the (π, 0) and (0, π) points, deviating therefore from the conventional d-wave form in striking similarity with recent experimental data. An instability in the triplet superconducting channel is much weaker than the singlet one and has an f-wave like form of the gap function.
We consider formulations of the functional renormaliztion-group flow for correlated electronic sy... more We consider formulations of the functional renormaliztion-group flow for correlated electronic systems, having the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting the one-particle irreducible (with respect to the local Green functions) six-point vertices and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF 2 RG approach [Phys. Rev. Lett. 112, 196402 (2014)], but also by the scale-dependent generalization of the one-particle irreducible (with respect to local Green functions, 1PI-LGF) representation of the generating functional [Phys. Rev. B 88, 115112 (2013)]. The second class is represented by the fRG flow within the dual fermion (DF) approach [Phys. Rev. B 77, 033101 (2008); ArXiv 1411.1342]. We compare formulations of fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard mo...
I consider the fulfillment of conservation laws and Ward identities in the one-and two-loop funct... more I consider the fulfillment of conservation laws and Ward identities in the one-and two-loop functional renormalization group approach. It is shown that in a one-particle irreducible scheme of this approach Ward identities are fulfilled only with the accuracy of the neglected two-loop terms O(V 3 Λ ) at oneloop order, and with the accuracy O(V 4 Λ ) at two-loop order (VΛ is the effective interaction vertex at scale Λ). The oneparticle self-consistent version of the two-loop RG equations which leads to smaller errors in Ward identities due to the absence of the terms with non-overlapping loops, is proposed. In particular, these modified equations exactly satisfy Ward identities in the ladder approximation.
The self-energy, spectral functions and susceptibilities of 2D systems with strong ferromagnetic ... more The self-energy, spectral functions and susceptibilities of 2D systems with strong ferromagnetic fluctuations are considered within the quasistatic approach. The self-energy at low temperatures T has a non-Fermi liquid form in the energy window |ω| ∆0 near the Fermi level, where ∆0 is the groundstate spin splitting for magnetically ordered ground state, and ∆0 ∝ T 1/2 ln 1/2 (vF /T ) in the quantum critical regime (vF is the Fermi velocity). Spectral functions have a two-peak structure at finite T above the magnetically ordered ground state, which implies quasi-splitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations. The triplet pairing amplitude in the quasistatic approximation increases with increasing correlation length; at low temperatures T ≪ ∆0 the vertex corrections become important and the Eliashberg approach is not justified. The results for the spectral properties and susceptibilities in the quantum critical regime near charge-(spin-) instabilities with large enough correlation length ξ ≫ (T /vF ) −1/3 are obtained.
We analyse the momentum dependence of static non-uniform susceptibilities of layered localmoment ... more We analyse the momentum dependence of static non-uniform susceptibilities of layered localmoment systems below Curie (Neel) temperature within the 1/S expansion, the renormalizationgroup approach, and first order of 1/N expansion. We argue that the previously known results of the spin-wave theory and renormalization-group approach for the transverse spin susceptibility acquire strong corrections already at sufficiently low temperatures, which appear due to the interaction of the incomping magnon having momentum q with magnons with momenta k < q. Such corrections can not be treated in the standard renormalization-group approach, but can be described by both, 1/S and 1/N expansions. The results of these expansions can be successfully extrapolated to T = TM , yielding the correct weight of static spin fluctuations, determined by the O(3) symmetry. For the longitudinal susceptibility, the summation of leading terms of 1/S expansion within the parquet approach allows to fulfill the sumrule for the weights of transverse and longitudinal fluctuations in a broad temperature region below TM outside the critical regime. We also discuss the effect of longitudinal spin fluctuations on the (sublattice) magnetization of layered systems.
We consider the application of the two-loop functional renormalization-group (fRG) approach to st... more We consider the application of the two-loop functional renormalization-group (fRG) approach to study the low-dimensional Hubbard model. This approach accounts for both, the universal and non-universal contributions to the RG flow. While the universal contributions were studied previously within the field-theoretical RG for the one-dimensional Hubbard model with linearized electronic dispersion and the two-dimensional Hubbard model with flat Fermi surface, the nonuniversal contributions to the flow of the vertices and susceptibilities appear to be important at large momenta scales. The two-loop fRG approach is also applied to the two-dimensional Hubbard model with a curved Fermi surface and the van Hove singularities near the Fermi level. The vertices and susceptibilities in the end of the flow of the two-loop approch are suppressed in comparison with both the one-loop approach with vertex projection and the modified one-loop approach with corrected vertex projection errors. The results of the two-loop approach are closer to the results of one-loop approach with the projected vertices, the difference of the results of one-and two-loop fRG approaches decreases when going away from the van Hove band filling. The quasiparticle weight remains finite in two dimensions at not too low temperatures above the paramagnetic ground state.
The interplay of magnetic and superconducting fluctuations in two dimensional systems with van Ho... more The interplay of magnetic and superconducting fluctuations in two dimensional systems with van Hove singularities in the electronic spectrum is considered within the functional renormalization group (fRG) approach. While the fRG flow has to be stoped at a certain minimal temperature T min RG , we study temperature dependence of magnetic and superconducting susceptibilities both, above and below T min RG , which allows to obtain the resulting ground state phase diagram. Close to half filling the fRG approach yields two quantum phase transitions: from commensurate antiferromagnetic to incommensurate phase and from the incommensurate to paramagnetic phase, the region of the commensurate magnetic phase is possibly phase separated away from half filling. Similarly to results of Hertz-Moriya-Millis approach, the temperature dependence of the inverse (incommensurate) magnetic susceptibility at the quantum phase transition from incommensurate to paramagnetic phase is found almost linear in temperature.
Journal of Physics A: Mathematical and Theoretical, 2013
We formulate the dual fermion approach for strongly correlated electronic systems in terms of the... more We formulate the dual fermion approach for strongly correlated electronic systems in terms of the lattice and dual effective interactions, obtained by using the covariation splitting formula. This allows us to consider the effect of six-point one-particle reducible interactions, which are usually neglected by the dual fermion approach. We show that the consideration of one-particle reducible six-point (as well as higher order) vertices is crucially important for the diagrammatic consistency of this approach. In particular, the relation between the dual and lattice self-energy, derived in the dual fermion approach, implicitly accounts for the effect of the diagrams, containing 6-point and higher order local one-particle reducible vertices, and should be applied with caution, if these vertices are neglected. Apart from that, the treatment of the self-energy feedback is also modified by 6-point and higher order vertices; these vertices are also important to account for some non-local corrections to the lattice self-energy, which have the same order in the local 4-point vertices, as the diagrams usually considered in the approach. These observations enlighten an importance of 6point and higher order vertices in the dual fermion approach, and call for development of new schemes of treatment of non-local fluctuations, which are based on one-particle irreducible quantities.
Journal of Physics A: Mathematical and Theoretical, 2011
I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatm... more I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider Polchinskii or Wick-ordered schemes with amputation of full (instead of bare) Green functions, as well as more general schemes, and eastablish their relation to the 'dynamical adjustment propagator' scheme by M. Salmhofer [Ann. der Phys. 16, 171 (2007)]. While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is not also evident, how the mean-field (MF) solution of these problems is recovered in this scheme. For Wick ordered scheme, excluding fully or partly tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize usefullness of the schemes, which are local in cutoff parameter, and compare them to the one-particle irreducible approach.
Applying the local density approximation (LDA) and dynamical mean field theory (DMFT) to paramagn... more Applying the local density approximation (LDA) and dynamical mean field theory (DMFT) to paramagnetic α-iron, we revisit a problem of theoretical description of its magnetic properties. The analysis of local magnetic susceptibility shows that at sufficiently low temperatures T < 1500 K, both, eg and t2g states equally contribute to the formation of the effective magnetic moment with spin S = 1. The self-energy of t2g states shows sizable deviations from Fermi-liquid form, which accompanies earlier found non-quasiparticle form of eg states. By considering the non-uniform magnetic susceptibility we find that the non-quasiparticle form of eg states is crucial for obtaining ferromagnetic instability in α-iron. The main contribution to the exchange interaction, renormalized by the effects of electron interaction, comes from the hybridization between t2g and eg states. We furthermore suggest the effective spin-fermion model for α-iron, which allows us to estimate the exchange interaction from paramagnetic phase, which is in agreement with previous calculations in the ordered state within the LDA approaches.
Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions ar... more Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient D in the spin-wave spectrum E k ∼ Dk 2 vanishes. Within the Dyson-Maleev formalism it is found that at low temperatures thermal fluctuations stabilize ferromagnetism by increasing the value of D. For not too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. Anomalous temperature behavior of magnetization is confirmed by Monte Carlo simulation. Strong field dependence of magnetization (paraprocess) at finite temperature is found near the frustration point.
The book is devoted to describing theoretical approaches to magnetism of two-dimensional systems:... more The book is devoted to describing theoretical approaches to magnetism of two-dimensional systems: mean-field theory, spin-fermion model, renormalization-group approach, and dynamic vertex approximation. Starting from the classical approaches by Stoner and Overhauser, but pointing the attention of the reader to their peculiarities in application to low-dimensional systems, described by the Hubbard model, the authors consider then the effect of magnetic fluctuations in these systems. Using the abovementioned approaches, the phase diagrams and magnetic properties of itinerant systems are analyzed in details. The book contains many results obtained by the authors, together with the overview of other existing approaches. It can be ordered from the authors (write by E-mail please).
We present a general frame to extend functional renormalization group (fRG) based computational s... more We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this solution accounts for a non-perturbative inclusion of correlations. Introducing auxiliary fermionic fields by means of a Hubbard-Stratonovich transformation, we derive the flow equations for the auxiliary fields and determine the relation to the conventional weak-coupling truncation of the hierarchy of flow equations. As a specific example we consider the dynamical mean-field theory (DMFT) solution as reference system, and discuss the relation to the recently introduced DMF 2 RG and the dual-fermion formalism.
Critical exponents in the CP N−1 model, which describes localized-moment ferro-and antiferromagne... more Critical exponents in the CP N−1 model, which describes localized-moment ferro-and antiferromagnets (N = 2 in the Heisenberg model), are calculated from two-particle Green's functions to first order in 1/N . For d = 2 + ε the results agree with earlier renormalization group calculations. For d = 3 the leading 1/N -corrections turn out to be very large at N = 2. For d = 4 − ε the 1/N -corrections are small at any N and insufficient to describe correctly the magnetic phase transition.
The nonlinear sigma-model and its generalization on N -component spins, the O(N ) model, are cons... more The nonlinear sigma-model and its generalization on N -component spins, the O(N ) model, are considered to describe thermodynamics of a quantum quasi-twodimensional (quasi-2D) Heisenberg antiferromagnet. A comparison with standard spin-wave approaches is performed. The sublattice magnetization, Neel temperature and spin correlation function are calculated to first order of the 1/N -expansion. A description of crossover from a 2D-like to 3D regime of sublattice magnetization temperature dependence is obtained. The values of the critical exponents derived are β = 0.36, η = 0.09. An account of the corrections to the standard logarithmic term of the spin-wave theory modifies considerably the value of the Neel temperature. The thermodynamic quantities calculated are universal functions of the renormalized interlayer coupling parameter. The renormalization of interlayer coupling parameter turns out to be considerably temperature dependent. A good agreement with experimental data on La 2 CuO 4 is obtained. The application of the approach used to the case of a ferromagnet is discussed. 75.10.Jm, 75.40.Cx
... In particular, the short-range magnetic order at temperatures above the magnetic-transition p... more ... In particular, the short-range magnetic order at temperatures above the magnetic-transition point is not completely destroyed (in the two-dimensional case it is retained at temperatures up to T $jJ j), so that there exists a wide temperature range T &amp;gt; TM with a strong short-range ...
A generalized supersymmetric representation of the Hubbard operator algebra is considered. This r... more A generalized supersymmetric representation of the Hubbard operator algebra is considered. This representation is applied to the infinite-U Hubbard model. A mean-field theory which takes into account both on-site and inter-site virtual boson-fermion transitions is developed. Unlike previous approaches, the mean-field theory considered is free from divergences. Possible application of these results to the ferromagnet-paramagnet transition, as well as to other problems is discussed.
The problem of the symmetry of the superconducting pairing and the form of the gap function in th... more The problem of the symmetry of the superconducting pairing and the form of the gap function in the electron-doped superconductors is reconsidered within the temperature-cutoff functional renormalization group approach combined with the Bethe-Salpeter equations. The momentum dependence of the order parameter for antiferromagnetic and superconducting instabilities in these compounds is analyzed. The gap function in the antiferromagnetic (particle-hole) channel has its maxima at the hot-spots, or at the diagonal of the Brilloin zone in their absence. The wavefunction in the singlet superconducting channel is non-monotonic in the vicinity of the (π, 0) and (0, π) points, deviating therefore from the conventional d-wave form in striking similarity with recent experimental data. An instability in the triplet superconducting channel is much weaker than the singlet one and has an f-wave like form of the gap function.
We consider formulations of the functional renormaliztion-group flow for correlated electronic sy... more We consider formulations of the functional renormaliztion-group flow for correlated electronic systems, having the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting the one-particle irreducible (with respect to the local Green functions) six-point vertices and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF 2 RG approach [Phys. Rev. Lett. 112, 196402 (2014)], but also by the scale-dependent generalization of the one-particle irreducible (with respect to local Green functions, 1PI-LGF) representation of the generating functional [Phys. Rev. B 88, 115112 (2013)]. The second class is represented by the fRG flow within the dual fermion (DF) approach [Phys. Rev. B 77, 033101 (2008); ArXiv 1411.1342]. We compare formulations of fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard mo...
I consider the fulfillment of conservation laws and Ward identities in the one-and two-loop funct... more I consider the fulfillment of conservation laws and Ward identities in the one-and two-loop functional renormalization group approach. It is shown that in a one-particle irreducible scheme of this approach Ward identities are fulfilled only with the accuracy of the neglected two-loop terms O(V 3 Λ ) at oneloop order, and with the accuracy O(V 4 Λ ) at two-loop order (VΛ is the effective interaction vertex at scale Λ). The oneparticle self-consistent version of the two-loop RG equations which leads to smaller errors in Ward identities due to the absence of the terms with non-overlapping loops, is proposed. In particular, these modified equations exactly satisfy Ward identities in the ladder approximation.
The self-energy, spectral functions and susceptibilities of 2D systems with strong ferromagnetic ... more The self-energy, spectral functions and susceptibilities of 2D systems with strong ferromagnetic fluctuations are considered within the quasistatic approach. The self-energy at low temperatures T has a non-Fermi liquid form in the energy window |ω| ∆0 near the Fermi level, where ∆0 is the groundstate spin splitting for magnetically ordered ground state, and ∆0 ∝ T 1/2 ln 1/2 (vF /T ) in the quantum critical regime (vF is the Fermi velocity). Spectral functions have a two-peak structure at finite T above the magnetically ordered ground state, which implies quasi-splitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations. The triplet pairing amplitude in the quasistatic approximation increases with increasing correlation length; at low temperatures T ≪ ∆0 the vertex corrections become important and the Eliashberg approach is not justified. The results for the spectral properties and susceptibilities in the quantum critical regime near charge-(spin-) instabilities with large enough correlation length ξ ≫ (T /vF ) −1/3 are obtained.
We analyse the momentum dependence of static non-uniform susceptibilities of layered localmoment ... more We analyse the momentum dependence of static non-uniform susceptibilities of layered localmoment systems below Curie (Neel) temperature within the 1/S expansion, the renormalizationgroup approach, and first order of 1/N expansion. We argue that the previously known results of the spin-wave theory and renormalization-group approach for the transverse spin susceptibility acquire strong corrections already at sufficiently low temperatures, which appear due to the interaction of the incomping magnon having momentum q with magnons with momenta k < q. Such corrections can not be treated in the standard renormalization-group approach, but can be described by both, 1/S and 1/N expansions. The results of these expansions can be successfully extrapolated to T = TM , yielding the correct weight of static spin fluctuations, determined by the O(3) symmetry. For the longitudinal susceptibility, the summation of leading terms of 1/S expansion within the parquet approach allows to fulfill the sumrule for the weights of transverse and longitudinal fluctuations in a broad temperature region below TM outside the critical regime. We also discuss the effect of longitudinal spin fluctuations on the (sublattice) magnetization of layered systems.
We consider the application of the two-loop functional renormalization-group (fRG) approach to st... more We consider the application of the two-loop functional renormalization-group (fRG) approach to study the low-dimensional Hubbard model. This approach accounts for both, the universal and non-universal contributions to the RG flow. While the universal contributions were studied previously within the field-theoretical RG for the one-dimensional Hubbard model with linearized electronic dispersion and the two-dimensional Hubbard model with flat Fermi surface, the nonuniversal contributions to the flow of the vertices and susceptibilities appear to be important at large momenta scales. The two-loop fRG approach is also applied to the two-dimensional Hubbard model with a curved Fermi surface and the van Hove singularities near the Fermi level. The vertices and susceptibilities in the end of the flow of the two-loop approch are suppressed in comparison with both the one-loop approach with vertex projection and the modified one-loop approach with corrected vertex projection errors. The results of the two-loop approach are closer to the results of one-loop approach with the projected vertices, the difference of the results of one-and two-loop fRG approaches decreases when going away from the van Hove band filling. The quasiparticle weight remains finite in two dimensions at not too low temperatures above the paramagnetic ground state.
The interplay of magnetic and superconducting fluctuations in two dimensional systems with van Ho... more The interplay of magnetic and superconducting fluctuations in two dimensional systems with van Hove singularities in the electronic spectrum is considered within the functional renormalization group (fRG) approach. While the fRG flow has to be stoped at a certain minimal temperature T min RG , we study temperature dependence of magnetic and superconducting susceptibilities both, above and below T min RG , which allows to obtain the resulting ground state phase diagram. Close to half filling the fRG approach yields two quantum phase transitions: from commensurate antiferromagnetic to incommensurate phase and from the incommensurate to paramagnetic phase, the region of the commensurate magnetic phase is possibly phase separated away from half filling. Similarly to results of Hertz-Moriya-Millis approach, the temperature dependence of the inverse (incommensurate) magnetic susceptibility at the quantum phase transition from incommensurate to paramagnetic phase is found almost linear in temperature.
Journal of Physics A: Mathematical and Theoretical, 2013
We formulate the dual fermion approach for strongly correlated electronic systems in terms of the... more We formulate the dual fermion approach for strongly correlated electronic systems in terms of the lattice and dual effective interactions, obtained by using the covariation splitting formula. This allows us to consider the effect of six-point one-particle reducible interactions, which are usually neglected by the dual fermion approach. We show that the consideration of one-particle reducible six-point (as well as higher order) vertices is crucially important for the diagrammatic consistency of this approach. In particular, the relation between the dual and lattice self-energy, derived in the dual fermion approach, implicitly accounts for the effect of the diagrams, containing 6-point and higher order local one-particle reducible vertices, and should be applied with caution, if these vertices are neglected. Apart from that, the treatment of the self-energy feedback is also modified by 6-point and higher order vertices; these vertices are also important to account for some non-local corrections to the lattice self-energy, which have the same order in the local 4-point vertices, as the diagrams usually considered in the approach. These observations enlighten an importance of 6point and higher order vertices in the dual fermion approach, and call for development of new schemes of treatment of non-local fluctuations, which are based on one-particle irreducible quantities.
Journal of Physics A: Mathematical and Theoretical, 2011
I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatm... more I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider Polchinskii or Wick-ordered schemes with amputation of full (instead of bare) Green functions, as well as more general schemes, and eastablish their relation to the 'dynamical adjustment propagator' scheme by M. Salmhofer [Ann. der Phys. 16, 171 (2007)]. While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is not also evident, how the mean-field (MF) solution of these problems is recovered in this scheme. For Wick ordered scheme, excluding fully or partly tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize usefullness of the schemes, which are local in cutoff parameter, and compare them to the one-particle irreducible approach.
Applying the local density approximation (LDA) and dynamical mean field theory (DMFT) to paramagn... more Applying the local density approximation (LDA) and dynamical mean field theory (DMFT) to paramagnetic α-iron, we revisit a problem of theoretical description of its magnetic properties. The analysis of local magnetic susceptibility shows that at sufficiently low temperatures T < 1500 K, both, eg and t2g states equally contribute to the formation of the effective magnetic moment with spin S = 1. The self-energy of t2g states shows sizable deviations from Fermi-liquid form, which accompanies earlier found non-quasiparticle form of eg states. By considering the non-uniform magnetic susceptibility we find that the non-quasiparticle form of eg states is crucial for obtaining ferromagnetic instability in α-iron. The main contribution to the exchange interaction, renormalized by the effects of electron interaction, comes from the hybridization between t2g and eg states. We furthermore suggest the effective spin-fermion model for α-iron, which allows us to estimate the exchange interaction from paramagnetic phase, which is in agreement with previous calculations in the ordered state within the LDA approaches.
Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions ar... more Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient D in the spin-wave spectrum E k ∼ Dk 2 vanishes. Within the Dyson-Maleev formalism it is found that at low temperatures thermal fluctuations stabilize ferromagnetism by increasing the value of D. For not too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. Anomalous temperature behavior of magnetization is confirmed by Monte Carlo simulation. Strong field dependence of magnetization (paraprocess) at finite temperature is found near the frustration point.
The book is devoted to describing theoretical approaches to magnetism of two-dimensional systems:... more The book is devoted to describing theoretical approaches to magnetism of two-dimensional systems: mean-field theory, spin-fermion model, renormalization-group approach, and dynamic vertex approximation. Starting from the classical approaches by Stoner and Overhauser, but pointing the attention of the reader to their peculiarities in application to low-dimensional systems, described by the Hubbard model, the authors consider then the effect of magnetic fluctuations in these systems. Using the abovementioned approaches, the phase diagrams and magnetic properties of itinerant systems are analyzed in details. The book contains many results obtained by the authors, together with the overview of other existing approaches. It can be ordered from the authors (write by E-mail please).
We present a general frame to extend functional renormalization group (fRG) based computational s... more We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this solution accounts for a non-perturbative inclusion of correlations. Introducing auxiliary fermionic fields by means of a Hubbard-Stratonovich transformation, we derive the flow equations for the auxiliary fields and determine the relation to the conventional weak-coupling truncation of the hierarchy of flow equations. As a specific example we consider the dynamical mean-field theory (DMFT) solution as reference system, and discuss the relation to the recently introduced DMF 2 RG and the dual-fermion formalism.
Critical exponents in the CP N−1 model, which describes localized-moment ferro-and antiferromagne... more Critical exponents in the CP N−1 model, which describes localized-moment ferro-and antiferromagnets (N = 2 in the Heisenberg model), are calculated from two-particle Green's functions to first order in 1/N . For d = 2 + ε the results agree with earlier renormalization group calculations. For d = 3 the leading 1/N -corrections turn out to be very large at N = 2. For d = 4 − ε the 1/N -corrections are small at any N and insufficient to describe correctly the magnetic phase transition.
The nonlinear sigma-model and its generalization on N -component spins, the O(N ) model, are cons... more The nonlinear sigma-model and its generalization on N -component spins, the O(N ) model, are considered to describe thermodynamics of a quantum quasi-twodimensional (quasi-2D) Heisenberg antiferromagnet. A comparison with standard spin-wave approaches is performed. The sublattice magnetization, Neel temperature and spin correlation function are calculated to first order of the 1/N -expansion. A description of crossover from a 2D-like to 3D regime of sublattice magnetization temperature dependence is obtained. The values of the critical exponents derived are β = 0.36, η = 0.09. An account of the corrections to the standard logarithmic term of the spin-wave theory modifies considerably the value of the Neel temperature. The thermodynamic quantities calculated are universal functions of the renormalized interlayer coupling parameter. The renormalization of interlayer coupling parameter turns out to be considerably temperature dependent. A good agreement with experimental data on La 2 CuO 4 is obtained. The application of the approach used to the case of a ferromagnet is discussed. 75.10.Jm, 75.40.Cx
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