Metropolis Monte Carlo generalized algorithm

Because generalized Metropolis Monte Carlo methods are based on random sampling from probability distribution functions, it is necessary to use a high-quality random-number generator algorithm to obtain reliable results. A review of such methods is beyond the scope of this chapter, " but a few general considerations merit discussion. 

The strategy in Variational Monte Carlo (VMC) is therefore to pick a proper form for a trial wave function based on physical insight for the particular system under study. In general, a number of parameters (oi,..., a ) will appear in the wave function to be treated as variational parameters. For any given set of a the Metropolis algorithm is used to sample the distribution... 

Some new numerical results for fluid He, fluid He, and the hard-sphere fluid, under quantum diffraction effects, are given below to illustrate a number of the basic main points discussed in this chapter. The particle masses (amu) have been set to m( He) = 4.0026, m("He) = 3.01603, and m(hard sphere) = 28.0134. PIMC simulations in the canonical ensemble using the necklace normal-mode moves have been employed. The Metropolis algorithm has been apphed with the general acceptance criterion set to 50% of the attempted moves for each normal mode. In the helium simulations the propagator SCVJ (a = 1 / 3) has been utihzed. The quantum hard-sphere fluid results presented in this chapter have been obtained from a further processing of data reported in Ref. 96. Also, for fluid He Monte Carlo classical (CLAS) and effective potential QFH calculations have been performed by following the standard procedures. 

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