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...

Graphical representations similar to the FK representation are developed for a variety of spin-systems. In several cases, it is established that these representations have (FKG) monotonicity properties which enables characterization theorems for the uniqueness phase and the low-temperature phase...