General method to sample systems in the microcanonical ensemble using Monte Carlo simulations

Abstract: Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient simulation algorithms. Nevertheless, nature does not know about statistical ensembles and therefore it is desirable and a theoretical challenge to show how to perform numerical simulations in the microcanonical ensemble without the use of unphysical degrees of freedom. In this article, we present a straightforward applicable method based on the concepts of a configurational temperature estimator (Rugh Phys Rev Lett 78:772, 1997; Gutiérrez et al. J Phys A Math Theor 51:455003, 2018) and on stochastic dynamics, which is independent of the Monte Carlo update strategy, and can be implemented for both local update or cluster algorithms. We illustrate it by performing a numerical simulation of the two-dimensional XY-model, finding the equilibrium temperature of two spin subsystems initially at different temperatures when they are put into thermal contact. Graphic abstract: [Figure not available: see fulltext.].