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Monte Carlo in statistical physics refers to the application of the Monte Carlo method to problems in statistical physics, or statistical mechanics. ==Overview== The general motivation to use the Monte Carlo method in statistical physics is to evaluate a multivariable integral. The typical problem begins with a system for which the Hamiltonian is known, it is at a given temperature and it follows the Boltzmann statistics. To obtain the mean value of some macroscopic variable, say A, the general approach is to compute, over all the phase space, PS for simplicity, the mean value of A using the Boltzmann distribution: . where - a vector with all the degrees of freedom (for instance, for a mechanical system, ), and is the partition function. One possible approach to solve this multivariable integral is to exactly enumerate all possible configurations of the system, and calculate averages at will. This is done in exactly solvable systems, and in simulations of simple systems with few particles. In realistic systems, on the other hand, an exact enumeration can be difficult or impossible to implement. For those systems, the Monte Carlo integration (and not to be confused with Monte Carlo method, which is used to simulate molecular chains) is generally employed. The main motivation for its use is the fact that, with the Monte Carlo integration, the error goes as , independently of the dimension of the integral. Another important concept related to the Monte Carlo integration is the importance sampling, a technique that improves the computational time of the simulation. In the following sections, the general implementation of the Monte Carlo integration for solving this kind of problems is discussed. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Monte Carlo method in statistical physics」の詳細全文を読む スポンサード リンク
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