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The Markov chain Monte Carlo method as a statistical mechanics technique forthe study of macroscopic systems has furnished the scientific community withgreat knowledge and advances in the theory of phase transitions. While a numberof Monte Carlo models have been proposed for the study of surface growth, thesemodels have not nearly being studied as exhaustively as in the models ofmagnetic systems, a paradigm of which is the classical model of Ernest Ising.In particular, studies of phase transitions in surface/interface science atnanometric scales are almost non-existent. This article has been written tomotivate research in this area of statistical mechanics from the perspective ofsurface science. In this article we survey the rudiments of the method alongwith some models of disordered systems such as magnetic systems, materialfracture, nano-pattern formation under ion bombardment, and molecularchirality. We performed simulations of these models using the method andobtained results that are in excellent agreement with experimentalobservations.

Nanometric Scale Surface science and the Markov chain Monte Carlo simulation of disordered systems