A Machine Learning study of the two-dimensional antiferromagnetic Ising model with nearest and next-to-nearest interactions on the triangular lattice

TL;DR

This study employs a novel neural network training approach to accurately identify phase transition temperatures and their nature in a complex antiferromagnetic Ising model on a triangular lattice, confirming known results efficiently.

Contribution

Introduces an unconventional neural network training method that does not require real spin configurations, enabling accurate phase transition analysis in frustrated magnetic systems.

Findings

Critical temperatures accurately computed

Phase transitions identified as first order

Method confirmed consistent with previous results

Abstract

We study the phase transitions of the two-dimensional antiferromagnetic Ising model with nearest $J_1$ and next-to-nearest $J_2$ interactions on the triangular lattice for $J_2/J_1 = 0.1, 0.5$ and 1.0. The method of supervised neural networks (NN) is employed for the investigation. While supervised NN is used, no real spin configurations are needed for the training. In addition, two kinds of configurations having their spins be arranged in a staggered pattern are considered as the training set. Remarkably, with this unconventional training strategy, not only the critical temperatures of the studied $J_2/J_1$ are computed accurately by the resulting NN, but also the nature of the investigated phase transitions are determined correctly. Specifically, the phase transitions associated with $J_2/J_1 = 0.1, 0.5$ and 1.0 are first order. These conclusions are consistent with the known results obtained by other methods. Since the training strategy is simple, the NN calculations is highly efficient. It remains to examine whether the unconventional training approach considered in this study can be used to investigate other models with untypical phase transitions or with nontrivial ground state configurations.