Random-cluster model
The random-cluster (Fortuin–Kasteleyn) model and its Edwards–Sokal coupling with the Potts and Ising models: finite-volume measures, the FKG inequality and comparison with Bernoulli percolation, infinite-volume limits, translation invariance and ergodicity, the free energy, agreement of free and wired measures, and the critical point.
- Edwards–Sokal coupling and the FK representation
- Random-cluster measures on finite graphs
- FKG inequality and monotonicity of random-cluster measures
- Infinite-volume random-cluster measures
- Critical point of the random-cluster model
- Translation invariance and ergodicity of the q = 2 random-cluster measures
- Convexity of the free energy and edge densities
- Free energy of the random-cluster model
- Per-box agreement of free and wired random-cluster measures
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