Higher-order tensor renormalization group study of the $J_1$-$J_2$ Ising model on a square lattice

TL;DR

This study uses the higher-order tensor renormalization group method to analyze phase transitions in the $J_1$-$J_2$ Ising model on a square lattice, revealing nuanced transition behaviors and universality class deviations.

Contribution

It applies HOTRG to larger system sizes, providing new insights into the nature and width of first-order transitions and the universality class of second-order transitions in the $J_1$-$J_2$ Ising model.

Findings

First-order transition region is narrower than previously reported.

Second-order transition universality class may differ from Ashkin--Teller class.

Identification of weak first- and second-order transitions near $g=1/2$.

Abstract

Phase transitions of the $J_1$-$J_2$ Ising model on a square lattice are studied using the higher-order tensor renormalization group(HOTRG) method. This system involves a competition between the ferromagnetic interaction $J_1$ and antiferromagnetic interaction $J_2$. Furthermore, weak first-order and second-order transitions are observed near the ratio $g=J_2/|J_1|=1/2$. Our results (based on HOTRG calculations for significantly larger sizes) indicate that the region of the first-order transition is marginally narrower than that in previous studies. Moreover, the universality class of the second-order transition connected to the transition line is not necessarily fully consistent with the Ashkin--Teller class considered earlier.