Efficient sampling and counting algorithms for the Potts model on ℤᵈ at all temperatures

For d ≥ 2 and all q≥ q0(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 temperature β≥ 0. This stands in contrast to Markov chain mixing time results: the Glauber dynamics mix slowly at and below the critical temperature, and ...More