Introduction: Theory and “Technical” Aspects of Monte Carlo Simulations

An outline is given of the physical problems which can be treated by Monte Carlo sampling and which are described in the later chapters of this book. Then the theoretical background is described for the application of this technique to calculate statistical ensemble averages of classical interacting many-body systems. The practical realization of the method is discussed, as well as its limitations due to finite time averaging, finite size and boundary effects, etc. It is shown how to extract meaningful information from the “raw data” of such a “computer experiment”. The stochastic simulation of kinetic processes is also treated, with particular emphasis on the interpretation of the results near phase transitions in the system. Finally some approximative variants of the technique are discussed which might become useful to simulate critical phenomena.

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