Global Minimum Depth in Edwards-Anderson Model

Abstract

In the literature the most frequently cited data are quite contradictory, and there is no consensus on the global minimum value of 2D Edwards-Anderson (2D EA) Ising model. By means of computer simulations, with the help of exact polynomial Schraudolph-Kamenetsky algorithm, we examined the global minimum depth in 2D EA-type models. We found a dependence of the global minimum depth on the dimension of the problem N and obtained its asymptotic value in the limit N→∞. We believe these evaluations can be further used for examining the behavior of 2D Bayesian models often used in machine learning and image processing.