Critical frontier of the triangular antiferromagnet in a field

TL;DR

This paper investigates the critical behavior of the triangular antiferromagnetic Ising model in a magnetic field using transfer-matrix and Monte Carlo methods, comparing results with two theoretical models.

Contribution

It provides a detailed numerical analysis of the critical line and evaluates two competing theoretical predictions against the data.

Findings

Numerical data does not fit the vertex model prediction.

Data supports the Coulomb gas renormalization scenario.

Critical line shape aligns with the Coulomb gas theory.

Abstract

We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line with predictions of two different theoretical scenarios. Both scenarios, while plausible, involve assumptions. The first scenario is based on the generalization of the model to a vertex model, and the assumption that the exact analytic form of the critical manifold of this vertex model is determined by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights. However, it is not possible to fit the coefficients of such polynomials of orders up to 10, such as to reproduce the numerical data for the critical points. The second theoretical prediction is based on the assumption that a renormalization mapping exists of the Ising model on the Coulomb gas, and analysis of the resulting renormalization equations. It leads to a shape of the critical line that is inconsistent with the first prediction, but consistent with the numerical data.