Simulation algorithms for the random-cluster model

We compare the performance of Monte Carlo algorithms for the simulation of the random-cluster representation of the q-state Potts model for continuous values of q. In particular we consider a local bond update method, a statistical reweighting method of percolation configurations, and a cluster algorithm, all of which generate Boltzmann statistics. The dynamic exponent z of the cluster algorithm appears to be quite small, and to assume the values of the Swendsen-Wang algorithm for q = 2 and 3. The cluster algorithm appears to be much more efficient than our versions of the other two methods for the simulation of the random-cluster model. The higher efficiency of the cluster method with respect to the local method is primarily due to the fact that the computer time usage of the local method increases more rapidly with system size; the difference between the dynamic exponents is less important.