On a finite graph, the random-cluster model assigns an edge configuration probability proportional towhere count open edges, closed edges, and open connected components.
The Edwards-Sokal coupling assigns one common random spin to every random-cluster component. For it couples the random-cluster model to the Ising model.
A heat-bath Markov chain repeatedly chooses one coordinate and redraws it from its conditional distribution given all other coordinates. The target distribution is reversible and stationary for these updates.
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The Random Cluster Model is a mathematical model used primarily in statistical physics and probability theory to study statistical properties of systems exhibiting phase transitions. It is particularly relevant for understanding percolation, critical phenomena, and other related concepts in network theory and social dynamics. ### Basic Concepts: 1. **Clusters**: In the context of the model, a "cluster" refers to a group of connected nodes or sites in a network or lattice.