Critical temperature of a fully anisotropic three-dimensional Ising model

TL;DR

This paper calculates the critical temperature of a fully anisotropic 3D Ising model using transfer matrix and finite size scaling methods, providing new numerical results and an exact solution for a special case.

Contribution

It introduces a transfer matrix approach combined with finite size scaling for anisotropic 3D Ising models and derives an exact solution for a specific 2x2 case.

Findings

Calculated critical temperatures for anisotropic 3D Ising models.

Compared results with existing calculations.

Derived an exact analytical solution for the 2x2 anisotropic Ising chain.

Abstract

The critical temperature of a three-dimensional Ising model on a simple cubic lattice with different coupling strengths along all three spatial directions is calculated via the transfer matrix method and a finite size scaling for L x L oo clusters (L=2 and 3). The results obtained are compared with available calculations. An exact analytical solution is found for the 2 x 2 oo Ising chain with fully anisotropic interactions (arbitrary J_x, J_y and J_z).