Monte Carlo Studies of the HELIUM-4 Ground State and Liquids in Porous Media.

This thesis presents the results of two Monte Carlo simulations. The first is a study of the ground state of solid and liquid ^4He, using a shadow wavefunction. A new form of trial shadow wavefunction is introduced to describe this system. Monte Carlo integration was used to optimize the parameters of this function, and a thorough analysis of the shadow description of the system has been carried out. This shows improved pair correlations, an improved condensate fraction, substantially reduced variational energies and a good equation of state. The melting and freezing transition densities are found to be in good agreement with the exact results of Green's Function Monte Carlo (GFMC). A second shadow wavefunction is introduced in which a basis set expansion is used to optimize the two particle correlations. This shadow wavefunction yields pair correlation functions in excellent agreement with GFMC, as well as a substantial reduction in the variational energies at all densities. In the second part of this work, static critical phenomena of a 3D Ising model confined in a porous medium made by spinodal decomposition have been studied using large-scale Monte-Carlo simulations. The work explores the influence of the geometry of Vycor-like materials on liquid/vapor coexistence and the species separation of binary liquid mixtures. No surface lnteractions (preference of the Vycor-like material for one phase above the other) are taken into account. It was found that the critical temperature depends on the average pore size D as T _{c}(D) = T_{c }(infty) - c/D . The universality class of the phase transition is independent of the pore size, and the critical exponents obtained from our simulation data are upsilon = 0.8 +/- 0.1, gamma = 1.4 +/- 0.1, beta = 0.65 +/- 0.13. No divergence is observed in the specific heat, strongly suggesting that alpha <= 0. All data for all pore sizes can be collapsed well with the scaling function for the magnetic susceptibility chi L^{-gamma/ nu} = ~chi((T - T_{c}(D)/T_{c}(D))L ^{1/ nu}). These critical phenomena are consistent with those computed for the randomly diluted Ising model. Experimental realizations of the numerical experiments are discussed. To speed up the simulation of the Ising model in the porous medium, three parallel algorithms for simulating that model were introduced and implemented on the KSR-1 parallel computer. These are the parallel Metropolis algorithm, the parallel Swensen-Wang algorithm and the Parallel Local Cluster Algorithm. The parallel speedup that was obtained with each algorithm is presented, and the results discussed.