  The Markov chain Monte Carlo method as a statistical mechanics technique for
the study of macroscopic systems has furnished the scientific community with
great knowledge and advances in the theory of phase transitions. While a number
of Monte Carlo models have been proposed for the study of surface growth, these
models have not nearly being studied as exhaustively as in the models of
magnetic systems, a paradigm of which is the classical model of Ernest Ising.
In particular, studies of phase transitions in surface/interface science at
nanometric scales are almost non-existent. This article has been written to
motivate research in this area of statistical mechanics from the perspective of
surface science. In this article we survey the rudiments of the method along
with some models of disordered systems such as magnetic systems, material
fracture, nano-pattern formation under ion bombardment, and molecular
chirality. We performed simulations of these models using the method and
obtained results that are in excellent agreement with experimental
observations.
