Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models

TL;DR

This paper introduces a loop model reformulation of the O(N) sigma model, enabling efficient Monte Carlo simulations and demonstrating the universality of the continuum limit, with potential for broader application to lattice field theories.

Contribution

The paper presents a novel loop model formulation of the O(N) sigma model and a Monte Carlo update scheme, enhancing simulation efficiency and generalizability.

Findings

Efficient Monte Carlo simulation comparable to reflection cluster methods

Demonstration of universality through a variant action

Potential for extending to other lattice field theories

Abstract

We reformulate the O(N) sigma model as a loop model whose configurations are the all-order strong coupling graphs of the original model. The loop configurations are represented by a pointer list in the computer and a Monte Carlo update scheme is proposed. Sample simulations are reported and the method turns out to be similarly efficient as the reflection cluster method, but it has greater potential for systematic generalization to other lattice field theories. A variant action suggested by the method is also simulated and leads to a rather extreme demonstration of the concept of universality of the scaling or continuum limit.