Critical Finite-Size-Scaling Amplitudes of a Fully Anisotropic Three-Dimensional Ising Model

TL;DR

This study calculates critical finite-size-scaling amplitudes for a fully anisotropic 3D Ising model using transfer-matrix methods, analyzing their behavior as a function of interaction anisotropy.

Contribution

It extends previous work by computing additional critical amplitudes, including susceptibilities and derivatives, for the anisotropic 3D Ising model.

Findings

Critical amplitude combinations are studied as functions of anisotropy.

Amplitudes of susceptibilities and derivatives are calculated.

Behavior of universal amplitude ratios is analyzed.

Abstract

A fully anisotropic simple-cubic Ising lattice in the geometry of periodic cylinders $n\times n\times\infty$ is investigated by the transfer-matrix finite-size scaling method. In addition to the previously obtained critical amplitudes of the inverse correlation lengths and singular part of the free energy [M. A. Yurishchev, Phys. Rev. B 50, 13 533 (1994)], the amplitudes of the usual (``linear'') and nonlinear susceptibilities and the amplitude of the second derivative of the spin-spin inverse correlation length with respect to the external field are calculated. The behavior of critical amplitude combinations (which, in accordance with the Privman-Fisher equations, do not contain in their composition the nonuniversal metric coefficients and geometry prefactor) are studied as a function of the interaction anisotropy parameters.