The Continuum Potts Model at the Disorder-Order Transition -- a Study by Cluster Dynamics

We investigate the continuum q-Potts model at its transition point from the disordered to the ordered regime, with particular emphasis on the coexistence of disordered and ordered phases in the high-q case. We argue that occurrence of phase transition can be seen as percolation in the related random cluster representation, similarly to the lattice Potts model, and investigate the typical structure of clusters for high q. We also report on numerical simulations in two dimensions using a continuum version of the Swendsen-Wang algorithm, compare the results with earlier simulations which used the invaded cluster algorithm, and discuss implications on the geometry of clusters in the disordered and ordered phases.