The Sine Gordon Model: Perturbation Theory and Cluster Monte Carlo

TL;DR

This paper develops a perturbative expansion and a nearly critical slowing down-free Monte Carlo algorithm for the 2D lattice Sine Gordon model, enabling detailed analysis of its rough phase.

Contribution

It introduces a cluster Monte Carlo algorithm with minimal critical slowing down and applies it alongside perturbation theory to study the model's rough phase.

Findings

Derived lines of constant physics in the rough phase

Demonstrated the efficiency of the cluster algorithm

Validated perturbative results with Monte Carlo data

Abstract

We study the expansion of the surface thickness in the 2-dimensional lattice Sine Gordon model in powers of the fugacity z. Using the expansion to order z**2, we derive lines of constant physics in the rough phase. We describe and test a VMR cluster algorithm for the Monte Carlo simulation of the model. The algorithm shows nearly no critical slowing down. We apply the algorithm in a comparison of our perturbative results with Monte Carlo data.