Cluster simulations of loop models on two-dimensional lattices

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.

LaTex2e, 4 pages; includes 1 table and 2 figures. Totally rewritten in version 2, with new theory and new data. Version 3 as published in PRL