Critical Binder cumulant in two-dimensional anisotropic Ising models

TL;DR

This paper investigates the critical Binder cumulant in two-dimensional anisotropic Ising models using Monte Carlo simulations, exploring universal and nonuniversal features through scale transformations.

Contribution

It introduces a method to relate critical cumulant values across isotropic and anisotropic cases via scale transformations in rectangular geometries.

Findings

Critical cumulant values are determined for various anisotropic Ising models.

A scale transformation approach links cumulant values between isotropic and anisotropic models.

Universal and nonuniversal features of the critical cumulant are identified.

Abstract

The Binder cumulant at the phase transition of Ising models on square lattices with various ferromagnetic nearest and next-nearest neighbour couplings is determined using mainly Monte Carlo techniques. We discuss the possibility to relate the value of the critical cumulant in the isotropic, nearest neighbour and in the anisotropic cases to each other by means of a scale transformation in rectangular geometry, to pinpoint universal and nonuniversal features.