Critical Binder cumulant of two-dimensional Ising models

TL;DR

This paper investigates the critical Binder cumulant in 2D Ising models on square and triangular lattices, analyzing how boundary conditions and lattice details influence its value at phase transition.

Contribution

It provides a detailed analysis of the factors affecting the critical Binder cumulant and discusses methods to identify universal critical cumulant values.

Findings

Binder cumulant depends on boundary conditions and lattice structure

Critical cumulant values vary with interaction symmetry

Discussion on identifying universal critical cumulants

Abstract

The fourth-order cumulant of the magnetization, the Binder cumulant, is determined at the phase transition of Ising models on square and triangular lattices, using Monte Carlo techniques. Its value at criticality depends sensitively on boundary conditions, details of the clusters used in calculating the cumulant, and symmetry of the interactions or, here, lattice structure. Possibilities to identify generic critical cumulants are discussed.