Cluster Simulation of the O(N) loop model on the Honeycomb lattice

We study the O(N) loop model on the Honeycomb lattice with real value N ≥ 1 by means of a cluster algorithm. The formulation of the algorithm is based on the equivalence of the O(N) loop model and the low-temperature graphical representation of a N-color Ashkin-Teller model on the triangular lattice. The latter model with integer N can be simulated by means of an embedding Swendsen-Wang-type cluster method. By taking into account the symmetry among loops of different colors, we develop another version of the Swendsen-Wang-type method. This version allows the number of colors N to take any real value N ≥ 1. As an application,