Random-cluster multihistogram sampling for theq-state Potts model

Random-cluster multihistogram sampling for the q-state Potts model.

Using the random-cluster representation of the q-state Potts models we consider the pooling of data from cluster-update Monte Carlo simulations for different thermal couplings K and number of states per spin q. Proper combination of histograms allows for the evaluation of thermal averages in a broad range of K and q values, including noninteger values of q. Due to restrictions in the sampling p...

Sampling in Potts Model on Sparse Random Graphs

We study the problem of sampling almost uniform proper q-colorings in sparse Erdős-Rényi random graphs G(n, d/n), a research initiated by Dyer, Flaxman, Frieze and Vigoda [2]. We obtain a fully polynomial time almost uniform sampler (FPAUS) for the problem provided q > 3d + 4, improving the current best bound q > 5.5d [6]. Our sampling algorithm works for more generalized models and broader fam...

The Potts and random-cluster models

Dynamic Exponents for Potts Model Cluster Algorithms

We have studied the Swendsen-Wang and Wolff cluster update algorithms for the Ising model in 2, 3 and 4 dimensions. The data indicate simple relations between the specific heat and the Wolff autocorrelations, and between the magnetization and the Swendsen-Wang autocorrelations. This implies that the dynamic critical exponents are related to the static exponents of the Ising model. We also inves...

Differential Inequalities for Potts and Random-Cluster Processes

Let θ(J) be the order parameter of a (ferromagnetic) Potts or randomcluster process with bond-variables J = (Je : e ∈ K). We discuss differential inequalities of the form ∂θ ∂Je ≤ α(J) ∂θ ∂Jf for all e, f ∈ K. Such inequalities may be established for all random-cluster processes that satisfy the FKG inequality, possibly in the presence of many-body interactions (subject to certain necessary and...