Effective Field Theory of the Zero-Temperature Triangular-Lattice Antiferromagnet: A Monte Carlo Study

TL;DR

This paper constructs and verifies a continuum field theory for the zero-temperature triangular Ising antiferromagnet using Monte Carlo methods, confirming a Gaussian height variable model and analyzing defect interactions.

Contribution

It explicitly constructs the continuum field theory for the model and confirms the Gaussian height variable conjecture through Monte Carlo simulations.

Findings

The continuum theory is Gaussian in the height variable.

The height-height correlation function and stiffness constant are measured.

Defect interactions at finite temperatures follow a 2D Coulomb gas scenario.

Abstract

Using a Monte Carlo coarse-graining technique introduced by Binder et al., we have explicitly constructed the continuum field theory for the zero-temperature triangular Ising antiferromagnet. We verify the conjecture that this is a gaussian theory of the height variable in the interface representation of the spin model. We also measure the height-height correlation function and deduce the stiffness constant. In addition, we investigate the nature of defect-defect interactions at finite temperatures, and find that the two-dimensional Coulomb gas scenario applies at low temperatures.