A cluster Monte Carlo algorithm for 2-dimensional spin glasses

Abstract:A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 1002 down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e2βJ) and not as a power law as T↦Tc = 0.