We develop an efficient algorithmic approach for approximate counting and sampling in the
low-temperature regime of a broad class of statistical physics models on finite subsets of the …

We show for the first time that the mixing time of Glauber (single edge update) dynamics for
the random cluster model at q= 2 is bounded by a polynomial in the size of the underlying …

For d≥ 2 and all q≥ q 0 (d) we give an efficient algorithm to approximately sample from the
q-state ferromagnetic Potts and random cluster models on the torus (ℤ/n ℤ) d for any inverse …

We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and
Potts models on the integer lattice ℤ d. This dynamics is a widely used Markov chain that …

Sampling from the q-state ferromagnetic Potts model is a fundamental question in statistical
physics, probability theory, and theoretical computer science. On general graphs, this …

An important paradigm in the understanding of mixing times of Glauber dynamics for spin
systems is the correspondence between spatial mixing properties of the models and bounds …

We study dynamical aspects of the q‐state Potts model on an n× n box at its critical βc (q).
Heat‐bath Glauber dynamics and cluster dynamics such as Swendsen–Wang (that …

Glauber dynamics on spin systems are well known to suffer exponential slowdowns at low
temperatures due to the emergence of multiple metastable phases, separated by narrow …

We establish rapid mixing of the random-cluster Glauber dynamics on random\varDelta Δ-
regular graphs for all q ≥ 1 q≥ 1 and p< p_u (q,\varDelta) p< pu (q, Δ), where the threshold …

The study of crossing probabilities-ie probabilities of existence of paths crossing rectangles-
has been at the heart of the theory of two-dimensional percolation since its beginning. They …