We propose the finite-size scaling of correlation function in a finite system near its critical p... more We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance r in the finite system with size L, the correlation function can be written as the product of |r| -(d-2+η) and its finite-size scaling function of variables r/L and tL 1/ν , where t = (T -Tc)/Tc. The directional dependence of correlation function is nonnegligible only when |r| becomes compariable with L. This finite-size scaling of correlation function has been confirmed by correlation functions of the Ising model and the bond percolation in two-diemnional lattices, which are calculated by Monte Carlo simulation. We can use the finite-size scaling of correlation function to determine the critical point and the critical exponent η.
We investigate first-and second-order quantum phase transitions of the anisotropic quantum Rabi m... more We investigate first-and second-order quantum phase transitions of the anisotropic quantum Rabi model, in which the rotating-and counter-rotating terms are allowed to have different coupling strength. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches we extract the phase diagram, scaling functions, and critical exponents, which allows us to establish that the universality class at finite anisotropy is the same as the isotropic limit. We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are relevant in a variety of systems able to realize strong coupling between light and matter, such as circuit QED setups where a finite anisotropy appears quite naturally.
Using the finite-size scaling, we have investigated the percolation phase transitions of evolving... more Using the finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges. This model becomes the Erdős-Rényi network at p = 0.5 and the random network under the Achlioptas process at p = 1. Using both the fixed point of s2/s1 and the straight line of ln s1, where s1 and s2 are the reduced sizes of the largest and the second largest cluster, we demonstrate that the phase transitions of this model are continuous for 0.5 ≤ p ≤ 1. From the slopes of ln s1 and ln(s2/s1) ′ at the critical point we get the critical exponents β and ν, which depend on p. Therefore the universality class of this model should be characterized by p also.
Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. ... more Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of higher order cumulants of order parameter are fully presented. Binder ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. From low to high temperature through the critical point, the ratios of third order cumulants change their values from negative to positive in a valley shape, and ratios of fourth order cumulants oscillate around zero. The normalized ratios, like the Skewness and Kurtosis, do not diverge with correlation length, in contrary with corresponding cumulants. Applications of these characters in search critical point in relativistic heavy ion collisions are discussed.
Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. ... more Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of higher order cumulants of order parameter are fully presented. Binder ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. From low to high temperature through the critical point, the ratios of third order cumulants change their values from negative to positive in a valley shape, and ratios of fourth order cumulants oscillate around zero. The normalized ratios, like the Skewness and Kurtosis, do not diverge with correlation length, in contrary with corresponding cumulants. Applications of these characters in search critical point in relativistic heavy ion collisions are discussed.
Despite the development of sophisticated statistical and dynamical climate models, a relative lon... more Despite the development of sophisticated statistical and dynamical climate models, a relative long-term and reliable prediction of the Indian summer monsoon rainfall (ISMR) has remained a challenging problem. Toward achieving this goal, here we construct a series of dynamical and physical climate networks based on the global near-surface air temperature field. We show that some characteristics of the directed and weighted climate networks can serve as efficient long-term predictors for ISMR forecasting. The developed prediction method produces a forecasting skill of 0.54 (Pearson correlation) with a 5-month lead time by using the previous calendar year’s data. The skill of our ISMR forecast is better than that of operational forecasts models, which have, however, quite a short lead time. We discuss the underlying mechanism of our predictor and associate it with network–ENSO and ENSO–monsoon connections. Moreover, our approach allows predicting the all-India rainfall, as well as the ...
Proceedings of the National Academy of Sciences, 2019
Significance Although El Niño events characterized by anomalous episodic warmings of the eastern ... more Significance Although El Niño events characterized by anomalous episodic warmings of the eastern equatorial Pacific can trigger disasters in various parts of the globe, reliable forecasts of their magnitude are still limited to about 6 mo ahead. A significant extension of this prewarning time would be instrumental for mitigating some of the worst damages. Here we introduce an approach relying on information entropy, which achieves some doubling of the prewarning time. The approach is based on our finding that the entropy in one calendar year exhibits a strong correlation with the magnitude of an El Niño that starts in the following year and thus allows us to forecast the onset and the magnitude of an El Niño event 1 y in advance.
We analyze universal and nonuniversal finite-size effects of lattice systems in a L d geometry ab... more We analyze universal and nonuniversal finite-size effects of lattice systems in a L d geometry above the upper critical dimension d = 4 within the O(n) symmetric ϕ 4 lattice theory. On the basis of exact results for n → ∞ and one-loop results for n = 1 we identify significant lattice effects that cannot be explained by the ϕ 4 continuum theory. Our analysis resolves longstanding discrepancies between earlier asymptotic theories and Monte Carlo (MC) data for the five-dimensional Ising model of small size. We predict a nonmonotonic L dependence of the scaled susceptibility χL -d/2 at Tc with a weak maximum that has not yet been detected by MC data.
We have investigated both site and bond percolation on two-dimensional lattice under the random r... more We have investigated both site and bond percolation on two-dimensional lattice under the random rule and the product rule respectively. With the random rule, sites or bonds are added randomly into the lattice. From two candidates picked randomly, the site or bond with the smaller size product of two connected clusters is added when the product rule is taken. Not only the size of the largest cluster but also its size jump are studied to characterize the universality class of percolation. The finite-size scaling forms of giant cluster size and size jump are proposed and used to determine the critical exponents of percolation from Monte Carlo data. It is found that the critical exponents of both size and size jump in random site percolation are equal to that in random bond percolation. With the random rule, site and bond percolation belong to the same universality class. We obtain the critical exponents of the site percolation under the product rule, which are different from that of bo...
We propose a renormalization group (RG) theory of eigen microstates, which are introduced in the ... more We propose a renormalization group (RG) theory of eigen microstates, which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations. A microstate in the ensemble can be considered as a linear superposition of eigen microstates with probability amplitudes equal to their eigenvalues. Under the renormalization of a factor b, the largest eigenvalue σ 1 has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relation σ 1 b = b β / ν σ 1 , where β and ν are the critical exponents of order parameter and correlation length, respectively. With the Ising model in different dimensions, it has been demonstrated that the RG theory of eigen microstates is able to identify the critical point and to predict critical exponents and the universality class. Our theory can be used in research of critical phenomena both in equilibrium and non-equilibrium systems without considering the Hamiltonian, ...
In a hopper with cylindrical symmetry and an aperture of radius R, the vertical velocity of granu... more In a hopper with cylindrical symmetry and an aperture of radius R, the vertical velocity of granular flow v z depends on the distance from the hopper's center r and the height above the aperture z and v z = v z (r, z; R). We propose that the scaled vertical velocity v z (r, z; R)∕v z (0, 0; R) is a function of scaled variables r∕R r and z∕R z , where R r = R − 0.5d and R z = R − k 2 d with the granule diameter d and a parameter k 2 to be determined. After scaled by v 2 z (0, 0; R)∕R z , the effective acceleration a eff (r, z; R) derived from v z is a function of r∕R r and z∕R z also. The boundary condition a eff (0, 0; R) = − g of granular flows under earth gravity g gives rise to v z (0, 0; R) ∝ √ g � R − k 2 d � 1∕2. Our simulations using the discrete element method and GPU program in the three-dimensional and the two-dimensional hoppers confirm the size scaling relations of v z (r, z; R) and v z (0, 0; R). From the size scaling relations, we obtain the mass flow rate of D-dimensional hopper W ∝ √ g(R − 0.5d) D−1 (R − k 2 d) 1∕2 , which agrees with the Beverloo law at R ≫ d. It is the size scaling of vertical velocity field that results in the dimensional R-dependence of W in the Beverloo law.
We propose the finite-size scaling of correlation function in a finite system near its critical p... more We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance r in the finite system with size L, the correlation function can be written as the product of |r| -(d-2+η) and its finite-size scaling function of variables r/L and tL 1/ν , where t = (T -Tc)/Tc. The directional dependence of correlation function is nonnegligible only when |r| becomes compariable with L. This finite-size scaling of correlation function has been confirmed by correlation functions of the Ising model and the bond percolation in two-diemnional lattices, which are calculated by Monte Carlo simulation. We can use the finite-size scaling of correlation function to determine the critical point and the critical exponent η.
We investigate first-and second-order quantum phase transitions of the anisotropic quantum Rabi m... more We investigate first-and second-order quantum phase transitions of the anisotropic quantum Rabi model, in which the rotating-and counter-rotating terms are allowed to have different coupling strength. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches we extract the phase diagram, scaling functions, and critical exponents, which allows us to establish that the universality class at finite anisotropy is the same as the isotropic limit. We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are relevant in a variety of systems able to realize strong coupling between light and matter, such as circuit QED setups where a finite anisotropy appears quite naturally.
Using the finite-size scaling, we have investigated the percolation phase transitions of evolving... more Using the finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges. This model becomes the Erdős-Rényi network at p = 0.5 and the random network under the Achlioptas process at p = 1. Using both the fixed point of s2/s1 and the straight line of ln s1, where s1 and s2 are the reduced sizes of the largest and the second largest cluster, we demonstrate that the phase transitions of this model are continuous for 0.5 ≤ p ≤ 1. From the slopes of ln s1 and ln(s2/s1) ′ at the critical point we get the critical exponents β and ν, which depend on p. Therefore the universality class of this model should be characterized by p also.
Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. ... more Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of higher order cumulants of order parameter are fully presented. Binder ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. From low to high temperature through the critical point, the ratios of third order cumulants change their values from negative to positive in a valley shape, and ratios of fourth order cumulants oscillate around zero. The normalized ratios, like the Skewness and Kurtosis, do not diverge with correlation length, in contrary with corresponding cumulants. Applications of these characters in search critical point in relativistic heavy ion collisions are discussed.
Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. ... more Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of higher order cumulants of order parameter are fully presented. Binder ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. From low to high temperature through the critical point, the ratios of third order cumulants change their values from negative to positive in a valley shape, and ratios of fourth order cumulants oscillate around zero. The normalized ratios, like the Skewness and Kurtosis, do not diverge with correlation length, in contrary with corresponding cumulants. Applications of these characters in search critical point in relativistic heavy ion collisions are discussed.
Despite the development of sophisticated statistical and dynamical climate models, a relative lon... more Despite the development of sophisticated statistical and dynamical climate models, a relative long-term and reliable prediction of the Indian summer monsoon rainfall (ISMR) has remained a challenging problem. Toward achieving this goal, here we construct a series of dynamical and physical climate networks based on the global near-surface air temperature field. We show that some characteristics of the directed and weighted climate networks can serve as efficient long-term predictors for ISMR forecasting. The developed prediction method produces a forecasting skill of 0.54 (Pearson correlation) with a 5-month lead time by using the previous calendar year’s data. The skill of our ISMR forecast is better than that of operational forecasts models, which have, however, quite a short lead time. We discuss the underlying mechanism of our predictor and associate it with network–ENSO and ENSO–monsoon connections. Moreover, our approach allows predicting the all-India rainfall, as well as the ...
Proceedings of the National Academy of Sciences, 2019
Significance Although El Niño events characterized by anomalous episodic warmings of the eastern ... more Significance Although El Niño events characterized by anomalous episodic warmings of the eastern equatorial Pacific can trigger disasters in various parts of the globe, reliable forecasts of their magnitude are still limited to about 6 mo ahead. A significant extension of this prewarning time would be instrumental for mitigating some of the worst damages. Here we introduce an approach relying on information entropy, which achieves some doubling of the prewarning time. The approach is based on our finding that the entropy in one calendar year exhibits a strong correlation with the magnitude of an El Niño that starts in the following year and thus allows us to forecast the onset and the magnitude of an El Niño event 1 y in advance.
We analyze universal and nonuniversal finite-size effects of lattice systems in a L d geometry ab... more We analyze universal and nonuniversal finite-size effects of lattice systems in a L d geometry above the upper critical dimension d = 4 within the O(n) symmetric ϕ 4 lattice theory. On the basis of exact results for n → ∞ and one-loop results for n = 1 we identify significant lattice effects that cannot be explained by the ϕ 4 continuum theory. Our analysis resolves longstanding discrepancies between earlier asymptotic theories and Monte Carlo (MC) data for the five-dimensional Ising model of small size. We predict a nonmonotonic L dependence of the scaled susceptibility χL -d/2 at Tc with a weak maximum that has not yet been detected by MC data.
We have investigated both site and bond percolation on two-dimensional lattice under the random r... more We have investigated both site and bond percolation on two-dimensional lattice under the random rule and the product rule respectively. With the random rule, sites or bonds are added randomly into the lattice. From two candidates picked randomly, the site or bond with the smaller size product of two connected clusters is added when the product rule is taken. Not only the size of the largest cluster but also its size jump are studied to characterize the universality class of percolation. The finite-size scaling forms of giant cluster size and size jump are proposed and used to determine the critical exponents of percolation from Monte Carlo data. It is found that the critical exponents of both size and size jump in random site percolation are equal to that in random bond percolation. With the random rule, site and bond percolation belong to the same universality class. We obtain the critical exponents of the site percolation under the product rule, which are different from that of bo...
We propose a renormalization group (RG) theory of eigen microstates, which are introduced in the ... more We propose a renormalization group (RG) theory of eigen microstates, which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations. A microstate in the ensemble can be considered as a linear superposition of eigen microstates with probability amplitudes equal to their eigenvalues. Under the renormalization of a factor b, the largest eigenvalue σ 1 has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relation σ 1 b = b β / ν σ 1 , where β and ν are the critical exponents of order parameter and correlation length, respectively. With the Ising model in different dimensions, it has been demonstrated that the RG theory of eigen microstates is able to identify the critical point and to predict critical exponents and the universality class. Our theory can be used in research of critical phenomena both in equilibrium and non-equilibrium systems without considering the Hamiltonian, ...
In a hopper with cylindrical symmetry and an aperture of radius R, the vertical velocity of granu... more In a hopper with cylindrical symmetry and an aperture of radius R, the vertical velocity of granular flow v z depends on the distance from the hopper's center r and the height above the aperture z and v z = v z (r, z; R). We propose that the scaled vertical velocity v z (r, z; R)∕v z (0, 0; R) is a function of scaled variables r∕R r and z∕R z , where R r = R − 0.5d and R z = R − k 2 d with the granule diameter d and a parameter k 2 to be determined. After scaled by v 2 z (0, 0; R)∕R z , the effective acceleration a eff (r, z; R) derived from v z is a function of r∕R r and z∕R z also. The boundary condition a eff (0, 0; R) = − g of granular flows under earth gravity g gives rise to v z (0, 0; R) ∝ √ g � R − k 2 d � 1∕2. Our simulations using the discrete element method and GPU program in the three-dimensional and the two-dimensional hoppers confirm the size scaling relations of v z (r, z; R) and v z (0, 0; R). From the size scaling relations, we obtain the mass flow rate of D-dimensional hopper W ∝ √ g(R − 0.5d) D−1 (R − k 2 d) 1∕2 , which agrees with the Beverloo law at R ≫ d. It is the size scaling of vertical velocity field that results in the dimensional R-dependence of W in the Beverloo law.
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Papers by Xiaosong Chen