Pair correlations and structure factor of the $J_1$-$J_2$ square lattice Ising model in an external field within the Cluster Variation Method

TL;DR

This paper uses the Cluster Variation Method with a four point plaquette approximation to analyze the structure factor and phase transitions, including nematic phases, in the $J_1$-$J_2$ Ising model under an external field.

Contribution

It introduces a four point plaquette CVM approach to detect nematic phases and phase transitions in the $J_1$-$J_2$ Ising model, capturing orientational order.

Findings

Identifies signatures of nematic phases in the structure factor

Tracks phase transitions via maxima in the structure factor

Discusses the potential exactness of CVM on the disorder variety

Abstract

We compute the structure factor of the $J_1$-$J_2$ Ising model in an external field on the square lattice within the Cluster Variation Method. We use a four point plaquette approximation, which is the minimal one able to capture phases with broken orientational order in real space, like the recently reported Ising-nematic phase in the model. The analysis of different local maxima in the structure factor allows us to track the different phases and phase transitions against temperature and external field. Although the nematic susceptibility is not directly related to the structure factor, we show that because of the close relationship between the nematic order parameter and the structure factor, the latter shows unambiguous signatures of the presence of a nematic phase, in agreement with results from direct minimization of a variational free energy. The disorder variety of the model is identified and the possibility that the CVM four point approximation be exact on the disorder variety is discussed.