Test of Universality in Anisotropic 3D Ising Model

TL;DR

This study tests the universality principle in anisotropic 3D Ising models by comparing susceptibility ratios across different lattice configurations, finding no violation of universality as previously suggested.

Contribution

The paper provides the first direct comparison of susceptibility ratios in anisotropic 3D Ising models, challenging prior claims of universality violation.

Findings

No confirmation of universality violation in susceptibility ratios

Comparison between models with different neighbor interactions

Supports the universality principle in anisotropic 3D Ising models

Abstract

Chen and Dohm predicted theoretically in 2004 that the widely believed universality principle is violated in the Ising model on the simple cubic lattice with more than only six nearest neighbours. Schulte and Drope by Monte Carlo simulations found such violation, but not in the predicted direction. Selke and Shchur tested the square lattice. Here we check only this universality for the susceptibility ratio near the critical point. For this purpose we study first the standard Ising model on a simple cubic lattice with six nearest neighbours, then with six nearest and twelve next-nearest neighbours, and compare the results with the Chen-Dohm lattice of six nearest neighbours and only half of the twelve next-nearest neighbours. We do not confirm the violation of universality found by Schulte and Drope in the susceptibility ratio.