Cluster simulations of loop models on two-dimensional lattices

TL;DR

This paper introduces efficient cluster algorithms for two-dimensional loop models, enabling the study of critical phenomena and phase diagrams with minimal critical slowing-down for certain parameter ranges.

Contribution

The authors develop and apply novel cluster algorithms to loop models on 2D lattices, providing new insights into critical exponents and phase diagrams for O(n) models.

Findings

Algorithm reduces critical slowing-down for 1 ≤ n ≤ 2

New critical exponents determined for honeycomb-lattice O(n) model

Phase diagram details obtained for square-lattice O(n) model

Abstract

We develop cluster algorithms for a broad class of loop models on two-dimensional lattices, including several standard O(n) loop models at n \ge 1. We show that our algorithm has little or no critical slowing-down when 1 \le n \le 2. We use this algorithm to investigate the honeycomb-lattice O(n) loop model, for which we determine several new critical exponents, and a square-lattice O(n) loop model, for which we obtain new information on the phase diagram.