The critical Binder cumulant in a two--dimensional anisotropic Ising model with competing interaction

TL;DR

This paper investigates the critical Binder cumulant in a 2D anisotropic Ising model with competing interactions, using Monte Carlo simulations to analyze phase transition behavior and compare with renormalization group results.

Contribution

It provides the first detailed Monte Carlo analysis of the critical Binder cumulant in an anisotropic Ising model with competing interactions, highlighting the effect of interaction ratios.

Findings

Identification of the disorder line separating correlation regimes.

Variation of the critical cumulant with interaction strength ratio.

Comparison with renormalization group calculations.

Abstract

The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next--nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin--spin correlations. Findings on the variation of the critical cumulant with the ratio of the two interaction strengths are compared to related recent results based on renormalization group calculations.