Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models

In memory of Roland L. Dobrushin DECAY OF CORRELATIONS IN SUBCRITICAL POTTS AND RANDOM-CLUSTER MODELS

We prove exponential decay for the tail of the radius R of the cluster at the origin, for subcritical random-cluster models, under an assumption slightly weaker than that E(R d1) < 1 (here, d is the number of dimensions). Speciically, if E(R d1) < 1 throughout the subcritical phase, then P(R n) exp(n) for some > 0. This implies the exponential decay of the two-point correlation function of subc...

Correlation Functions for the 2d Random Bonds Potts Models

We study the spin-spin and energy-energy correlation functions for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach of the perturbation series around the conformal field theories representing the pure models. For the Ising model, we obtain a crossover in the amplitude for the correlation functions which d...

The Potts and random-cluster models

Coupling and Bernoullicity in random-cluster and Potts models

An explicit coupling construction of random-cluster measures is presented. As one of the applications of the construction, the Potts model on amenable Cayley graphs is shown to exhibit at every temperature the mixing property known as Bernoullicity.

Renormalisation group calculation of correlation functions for the 2D random bond Ising and Potts models

We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series around the conformal field theories representing the pure models. We obtain a crossover in the amplitude for the correlation function for the Ising model which d...