Cluster simulations of multi-spin Potts models

The Potts Hamiltonian provides a conceptually simple model of discrete variables with highly non-trivial properties. It has been studied extensively, and many of its properties are now well known. In this paper, we investigate a generalization of the Potts model to include multi-spin interactions. Following the work of Chayes and Machta, the Fortuin?Kastelyn transformation is generalized to enable us to use cluster methods in addition to the usual Metropolis algorithm for computer simulations. We have computed the critical properties of this model using both a finite-size scaling analysis with histograms and the Monte Carlo renormalization-group (MCRG) to determine the critical temperatures and exponents.