We consider Ising models on the hypercube with a general interaction matrix $ J $, and give
a polynomial time sampling algorithm when all but $ O (1) $ eigenvalues of $ J $ lie in an …

For Δ≥ 5 and q large as a function of Δ, we give a detailed picture of the phase transition of
the random cluster model on random Δ-regular graphs. In particular, we determine the …

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 give algorithms for approximating the partition function of the ferromagnetic $ q $-color
Potts model on graphs of maximum degree $ d $. Our primary contribution is a fully …

We propose a polynomial-time algorithm for preparing the Gibbs state of the two-
dimensional toric code Hamiltonian at any temperature, starting from any initial condition …

We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising
models with edge activities β> 1 and external fields λ< 1 (or symmetrically, λ> 1) on general …

By implementing algorithmic versions of Sapozhenko's graph container methods, we give
new algorithms for approximating the number of independent sets in bipartite graphs. Our …

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 …

A spin system is a framework in which the vertices of a graph are assigned spins from a finite
set. The interactions between neighbouring spins give rise to weights, so a spin assignment …

We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs
(or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation …