Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model

TL;DR

This paper investigates the critical Binder cumulant in an anisotropic 2D Ising model, demonstrating its dependence solely on the anisotropy's long-distance features and supporting universality in weakly anisotropic critical systems.

Contribution

The study provides a modified renormalization-group approach and confirms that the critical Binder cumulant depends only on the anisotropy's asymptotic properties, reinforcing universality claims.

Findings

U* depends only on the asymptotic critical anisotropy

Modified RG calculation accurately describes anisotropy dependence

Supports universality in weakly anisotropic critical phenomena

Abstract

We reanalyze transfer matrix and Monte Carlo results for the critical Binder cumulant U* of an anisotropic two-dimensional Ising model on a square lattice in a square geometry with periodic boundary conditions. Spins are coupled between nearest neighboring sites and between next-nearest neighboring sites along one of the lattice diagonals. We find that U* depends only on the asymptotic critical long-distance features of the anisotropy, irrespective of its realization through ferromagnetic or antiferromagnetic next-nearest neighbor couplings. We modify an earlier renormalization-group calculation to obtain a quantitative description of the anisotropy dependence of U*. Our results support our recent claim towards the validity of universality for critical phenomena in the presence of a weak anisotropy.