Critical Loop Gases and the Worm Algorithm

TL;DR

This paper explores the loop gas approach in lattice field theory, utilizing the worm algorithm for efficient Monte Carlo simulations, and studies the fractal and scaling properties of random loops with benchmarks from the Ising model.

Contribution

It introduces a novel application of percolation and self-avoiding walk theories to analyze the worm algorithm's estimators in loop gas models.

Findings

Fractal structure and scaling properties of loops are characterized.

The worm algorithm effectively samples loop configurations.

Benchmark results from the Ising model validate the approach.

Abstract

The loop gas approach to lattice field theory provides an alternative, geometrical description in terms of fluctuating loops. Statistical ensembles of random loops can be efficiently generated by Monte Carlo simulations using the worm update algorithm. In this paper, concepts from percolation theory and the theory of self-avoiding random walks are used to describe estimators of physical observables that utilize the nature of the worm algorithm. The fractal structure of the random loops as well as their scaling properties are studied. To support this approach, the O(1) loop model, or high-temperature series expansion of the Ising model, is simulated on a honeycomb lattice, with its known exact results providing valuable benchmarks.