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.

• Received 21 November 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.120601