Algorithmic overlaps as thermodynamic variables: from local to cluster Monte Carlo dynamics in critical phenomena (opens in new tab)

We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two successive Wolff clusters reflects critical behavior and can be used as an orde...