GRAPHICAL REPRESENTATIONS AND CLUSTER ALGORITHMS .1. DISCRETE SPIN SYSTEMS

Graphical representations similar to the FK representation are develop ed for a variety of spin-systems. Ln several cases, it is established that these representations have (FKG) monotonicity properties which en ables characterization theorems for the uniqueness phase and the low-t emperature phase of the spin system. Certain systems with intermediate phases and/or first-order transitions art: also described in terms of the percolation properties of the representations. In all cases, thes e representations lead. in a natural fashion, to Swendsen-Wang-type al gorithms. Hence, at least in the above-mentioned instances, these algo rithms realize the program described by Kandel and Domany. Phys, Rev, B 43 (1991) 8539-8548. All of the algorithms are shown to satisfy a Li -Sokal bound which (at least for systems with a divergent specific hea t implies critical slowing down. However, the representations also giv e rise to invaded cluster algorithms which may allow for the rapid sim ulation of some of these systems at their transition points.