Monte Carlo Study of Correlations Near the Ground State of the Triangular Antiferromagnetic Ising Model

TL;DR

This study investigates the spin-spin correlations in the ground state and near-ground state of the triangular antiferromagnetic Ising model using Monte Carlo simulations, analyzing how correlations evolve with temperature and system size.

Contribution

It introduces a finite-size scaling method using t=exp(-2/T) to analyze correlation functions near the ground state of the model.

Findings

Exact and Monte Carlo data agree on correlation decay at T=0.

Finite temperature modifies correlation decay due to finite correlation length.

Proposes a generalized correlation function for non-zero temperatures.

Abstract

We study the spin-spin correlation function in or near the T=0 ground state of the antiferromagnetic Ising model on a triangular lattice. At zero temperature its modulation on the sublattices gives rise to two Bragg peaks in the structure factor, and a known expression for the algebraic decay of correlations enables us to examine the form of the diffusive scattering. We do so by means of a comparison between exact results and data calculated using standard Monte Carlo techniques. At non-zero temperatures the finite correlation length alters this form, and we account for the change by proposing a generalisation of the zero temperature pair correlation function. The size dependence of our simulation data is investigated through a novel finite-size scaling analysis where t = exp(-2/T) is used as the temperature parameter.