Random-cluster multihistogram sampling for the q-state Potts model

Using the random-cluster representation of the q-state Potts models we consider the pooling of data from cluster-update Monte Carlo simulations for different thermal couplings K and number of states per spin q. Proper combination of histograms allows for the evaluation of thermal averages in a broad range of K and q values, including noninteger values of q. Due to restrictions in the sampling process correct normalization of the combined histogram data is nontrivial. We discuss the different possibilities and analyze their respective ranges of applicability.