Introduction

In recent years modeling methods based on computer simulation have become a useful tool in solving many scientific and engineering problems. Moreover, with the introduction of powerful workstations the impact of applications of computer simulation is expected to increase enormously in the next few years. To some extent, computer-based modeling methods have filled the long existing gap between experimental and theoretical divisions of natural sciences such as physics, chemistry, and biology. Such a dramatic role for computer simulation methods is due to the statistically exact character of information that they provide about the exactly defined model systems under study. The term “statistically exact information” means “information known within the range defined by standard deviation of some statistical distribution law.” This deviation can usually be reduced to an extent required by the problem under study. The term “exactly defined model” means that all parameters required to specify the model Hamiltonian are known exactly.

Let us specify the role of computer-based simulation with respect to information obtained by analytical derivation and experiment:

1. The analytically exact information is available only for a few theoretical models that allow exact analytical solutions. The most celebrated example of such a model in statistical physics is the two-dimensional Ising model for the nearest-neighbor interacting spins in the absence of external fields. Its analytically exact solution was obtained by Onsager (1944). However, in the majority of other cases, where exact analytical solutions are not known, it is customary to use different approximations. And it is often the case that these approximations are uncontrollable. The same Ising model in the three-dimensional case does not have an exact solution. Needless to say, even less is known about the models with more realistic intermolecular potentials. Therefore, computer simulation is often used to verify different approximations involved in analytical solutions.

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