First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions

TL;DR

This study uses a new numerical entropic scheme to analyze the first-order transition features of the triangular Ising model with competing interactions, confirming many theoretical predictions but also revealing discrepancies likely due to domain wall effects.

Contribution

The paper introduces a novel numerical entropic method to accurately characterize first-order transitions in the triangular Ising model with specific antiferromagnetic interactions, improving previous estimates and testing theoretical predictions.

Findings

Results support finite-size scaling predictions of first-order transitions.

Transition point shifts do not follow expected exponential behavior.

Double Gaussian approximation fails for higher energy cumulant corrections.

Abstract

We implement a new and accurate numerical entropic scheme to investigate the first-order transition features of the triangular Ising model with nearest-neighbor ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic interactions in ratio $R=J_{nn}/J_{nnn}=1$. Important aspects of the existing theories of first-order transitions are briefly reviewed, tested on this model, and compared with previous work on the Potts model. Using lattices with linear sizes $L=30,40,...,100,120,140,160,200,240,360$ and 480 we estimate the thermal characteristics of the present weak first-order transition. Our results improve the original estimates of Rastelli et al. and verify all the generally accepted predictions of the finite-size scaling theory of first-order transitions, including transition point shifts, thermal, and magnetic anomalies. However, two of our findings are not compatible with current phenomenological expectations. The behavior of transition points, derived from the number-of-phases parameter, is not in accordance with the theoretically conjectured exponentially small shift behavior and the well-known double Gaussian approximation does not correctly describe higher correction terms of the energy cumulants. It is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections.