Papers by Anthony Guttmann
Staircase polygons, elliptic integrals and Heun functions
Analysis of series expansions for non-algebraic singularities
Journal of Physics A: Mathematical and Theoretical, 2015
We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, s... more We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$
Correction to scaling exponents and critical properties of the n-vector model with dimensionality>4
J Phys a Math Gen, 1981
The high-temperature susceptibility and spin-spin correlation function of the three-dimensional Ising model
J Phys a Math Gen, 1987
The series analysis protocol developed in a preceding paper (ibid., vol.20, p.1839, 1987) is appl... more The series analysis protocol developed in a preceding paper (ibid., vol.20, p.1839, 1987) is applied to the susceptibility and correlation function of the three-dimensional Ising model. For the spin-1/2 Ising data, the author argues that the protocol needs modification to take account of trends in the data, which trends arise from the nature of the series. In this way the author obtains gamma =1.239+or-0.003 for all cubic lattices and for a variety of spin values. The diamond lattice data lies outside this range, and it is argued that this series is effectively far shorter than the others. The author also estimates nu =0.632+0.002-0.003 for the BCC lattice and obtains critical point estimates for all lattice and spin models studied.
On the recurrence relation method of series analysis
J Phys a Math Gen, 1975
Phase transitions in two dimensional isotropic spin systems
On the critical behaviour of self-avoiding walks. II
Journal of Physics a Mathematical and General, Jul 1, 1989
Ising model susceptibility amplitudes. I. Two-dimensional lattices
J Phys a Math Gen, 1975
Phys Rev B, 2003
For the study of Ising models of general spin S on the square lattice, we have combined our recen... more For the study of Ising models of general spin S on the square lattice, we have combined our recently extended high-temperature expansions with the low-temperature expansions derived some time ago by Enting, Guttmann, and Jensen. We have computed various critical parameters and improved the estimates of others. Moreover, the properties of hyperscaling and of universality (spin-S independence) of exponents and of various dimensionless amplitude combinations have been verified accurately. Assuming the validity of the lattice-lattice scaling, from our estimates of critical amplitudes for the square lattice we have also obtained estimates of the corresponding amplitudes for the spin-S Ising model on the triangular, honeycomb, and kagomé lattices.
Journal of Physics a Mathematical and Theoretical, Jun 28, 2010
We give a systematic treatment of lattice Green's functions (LGF) on the d-dimensional diamond, s... more We give a systematic treatment of lattice Green's functions (LGF) on the d-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality d >= 2 for the first three lattices, and for 2 <= d <= 5 for the hyper-fcc lattice. We show that there is a close connection between the LGF of the d-dimensional hyper-cubic lattice and that of the (d - 1)-dimensional diamond lattice. We give constant-term formulations of LGFs for each of these lattices in all dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the sc, bcc and diamond LGFs and some Ramanujan-type formulae for 1/Ï€.
A lattice model of superantiferromagnetism
Journal of Physics C Solid State Physics, 1972
The ordered phase of MnO, NiO and similar superantiferromagnetic materials leads to consideration... more The ordered phase of MnO, NiO and similar superantiferromagnetic materials leads to consideration of two lattice models of superantiferromagnetism derived from the Ising model. The first model is a simple cubic lattice with ferromagnetic interactions in the x and y directions and antiferromagnetic coupling in the z direction, while the second model has antiferromagnetic coupling in the x and y directions and ferromagnetic coupling in the z direction. It is shown that the absolute value of the critical temperature mod kTc/J mod is the same for both models, and is equal to that of the normal two sublattice model of antiferromagnetism, and that the critical exponents for both the susceptibility and specific heat are identical for both models, and equal to the corresponding exponents for the two sublattice model.
Phys Rev B, 1993
High-temperature-series expansions of the spin-spin correlation function for the plane-rotator (o... more High-temperature-series expansions of the spin-spin correlation function for the plane-rotator (or XY) model on the sc lattice are extended by three terms through order β17. Tables of the expansion coefficients are reported for the correlation function spherical moments of order l=0,1,2. Our analysis of the series leads to fairly accurate estimates of the critical parameters.
COMMENT: Comment on 'The exact location of partition function zeros, a new method for statistical mechanics
J Phys a Math Gen, 1987
Asymptotic analysis of power-series expan-sions
Ising model amplitudes and extended lattice-lattice scaling
J Phys a Math Gen, 1977
Math Comput Modelling, 1997
A polynomial time enumeration method for the three-choice polygon model in two dimensions is give... more A polynomial time enumeration method for the three-choice polygon model in two dimensions is given together with numerical analysis of the enumerated series and an argument supporting the asymptotic behaviour of the number of imperfect staircase polygons.
On the zero-field susceptibility in the d=4, n=0 limit: analysing for confluent logarithmic singularities
J Phys a Math Gen, 1978
On the critical behaviour of self-avoiding walks
J Phys a Math Gen, 1987
An Integral from Statistical Mechanics
Siam Rev, 1974
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Papers by Anthony Guttmann