It is argued that the leading corrections to scaling for planar Ising models, which occur as analytic factors, arise from the quadratic terms of the nonlinear thermal and ordering fields (rather than from irrelevant variables). This yields ${{\ensuremath{\alpha}}_{\mathrm{eff}}}^{\ensuremath{'}}+2{\ensuremath{\beta}}_{\mathrm{eff}}+{{\ensuremath{\gamma}}_{\mathrm{eff}}}^{\ensuremath{'}}=2$ for the effective critical exponents, with $\mathrm{no}$ leading corrections, and is confirmed by exact square-lattice results for arbitrary anisotropy $\frac{{J}_{2}}{{J}_{1}}$ . For isotropic lattices the ratios of correction amplitudes and quadratic nonlinear-field terms appear universal.It is argued that the leading corrections to scaling for planar Ising models, which occur as analytic factors, arise from the quadratic terms of the nonlinear thermal and ordering fields (rather than from irrelevant variables). This yields ${{\ensuremath{\alpha}}_{\mathrm{eff}}}^{\ensuremath{'}}+2{\ensuremath{\beta}}_{\mathrm{eff}}+{{\ensuremath{\gamma}}_{\mathrm{eff}}}^{\ensuremath{'}}=2$ for the effective critical exponents, with $\mathrm{no}$ leading corrections, and is confirmed by exact square-lattice results for arbitrary anisotropy $\frac{{J}_{2}}{{J}_{1}}$. For isotropic lattices the ratios of correction amplitudes and quadratic nonlinear-field terms appear universal.

Physical Review LettersSep 1, 198086 citations

On the corrections to scaling in three-dimensional Ising models

Andrea J. Liu, Michael Ellis Fisher

Journal of Statistical PhysicsFeb 1, 199077 citations

Universality in two-dimensional Ising models

Henk W. J. Blöte, M. P. Nightingale

Physica A Statistical Mechanics and its ApplicationsDec 1, 198540 citations

Universality in dynamic critical phenomena

Fu-Gao Wang, Chin‐Kun Hu

We use heat bath dynamics to evaluate the dynamic critical exponent $z$ and the dynamic finite-size scaling function of an Ising model on square, planar triangular, and honeycomb lattices. We find convincing evidence that $z$ is universal and, by choosing an aspect ratio and a nonuniversal metric factor for the scaled time of each lattice, we can obtain a universal dynamic finite-size scaling function for the Ising model on the planar lattices. Our results suggest many interesting problems for further research.We use heat bath dynamics to evaluate the dynamic critical exponent $z$ and the dynamic finite-size scaling function of an Ising model on square, planar triangular, and honeycomb lattices. We find convincing evidence that $z$ is universal and, by choosing an aspect ratio and a nonuniversal metric factor for the scaled time of each lattice, we can obtain a universal dynamic finite-size scaling function for the Ising model on the planar lattices. Our results suggest many interesting problems for further research.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsAug 1, 199773 citations

Universal amplitude ratios for scaling corrections on Ising strips

N. Sh. Izmailian

We study the (analytic) finite-size corrections in the Ising model on the strip with free, fixed (++), and mixed boundary conditions. For fixed (++) boundary conditions, the spins are fixed to the same values on two sides of the strip. We find that subdominant finite-size corrections to scaling should be to the form a(p)/N(2p-1) for the free energy f(N) and b(p)/N(2p-1) for inverse correlation length ξ(N)(-1), with integer value of p. We investigate the set {a(p),b(p)} by exact evaluation and their changes upon varying anisotropy of coupling. We find that the amplitude ratios b(p)/a(p) remain constant upon varying coupling anisotropy. Such universal behavior is correctly reproduced by the conformal perturbative approach.We study the (analytic) finite-size corrections in the Ising model on the strip with free, fixed (++), and mixed boundary conditions. For fixed (++) boundary conditions, the spins are fixed to the same values on two sides of the strip. We find that subdominant finite-size corrections to scaling should be to the form a(p)/N(2p-1) for the free energy f(N) and b(p)/N(2p-1) for inverse correlation length ξ(N)(-1), with integer value of p. We investigate the set {a(p),b(p)} by exact evaluation and their changes upon varying anisotropy of coupling. We find that the amplitude ratios b(p)/a(p) remain constant upon varying coupling anisotropy. Such universal behavior is correctly reproduced by the conformal perturbative approach.

Physical Review ENov 14, 20118 citations

Universality in Generalized Ising Models

WORLD SCIENTIFIC eBooksMar 1, 20080 citations

\mathrm{no}

leading corrections, and is confirmed by exact square-lattice results for arbitrary anisotropy

\frac{{J}_{2}}{{J}_{1}}

. For isotropic lattices the ratios of correction amplitudes and quadratic nonlinear-field terms appear universal.

We use heat bath dynamics to evaluate the dynamic critical exponent

z

and the dynamic finite-size scaling function of an Ising model on square, planar triangular, and honeycomb lattices. We find convincing evidence that

z

is universal and, by choosing an aspect ratio and a nonuniversal metric factor for the scaled time of each lattice, we can obtain a universal dynamic finite-size scaling function for the Ising model on the planar lattices. Our results suggest many interesting problems for further research.