Graphical representations and cluster algorithms II

We continue the study, initiated in Part I, of graphical representations and cluster algorithms for various models in (or related to) statistical mechanics. For certain models, e.g. the Blume–Emery–Griffths model and various generalizations, we develop Fortuin Kasteleyn-type representations which lead immediately to Swendsen Wang-type algorithms. For other models, e.g. the random cluster model, that are defined by a graphical representation, we develop cluster algorithms without reference to an underlying spin system. In all cases, phase transitions are related to percolation (or incipient percolation) in the graphical representation which, via the IC algorithm, allows for the rapid simulation of these systems at the transition point. Pertinent examples include the (continuum) Widom–Rowlinson model, the restricted 1-step solid-on-solid model and the XY model.