Benefits and pitfalls of belief-propagation-mediated superparamagnetic clustering

Belief propagation is a candidate for the accelerated evaluation of statistical averages if compared to Monte Carlo approaches. We show that superparamagnetic clustering can be accelerated substantially by means of belief propagation. However, critical slowing down of the method is observed. Origin and strategies of avoidance of the critical slowing down are explained from models of periodic Ising grids. We show that belief-propagation-mediated superparamagnetic clustering provides identical clusters with Monte Carlo-mediated clustering only at the coarse-grained level. Concurring results between the Monte Carlo and the belief-propagation methods can be obtained by means of the sequential superparamagnetic-clustering approach.