Phase Transitions in the Multicomponent Widom-Rowlinson Model and in Hard Cubes on the BCC--Lattice

We use Monte Carlo techniques and analytical methods to study the phase diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M greater or equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M) while for z > z_d(M) there are M demixed phases each consisting mostly of one species. For M=2 there is a direct second order transition from the gas phase to the demixed phase while for M greater or equal 3 the transition at z_d(M) appears to be first order putting it in the Potts model universality class. For M large, Pirogov-Sinai theory gives z_d(M) ~ M-2+2/(3M^2) + ... . In the crystal phase the particles preferentially occupy one of the sublattices, independent of species, i.e. spatial symmetry but not particle symmetry is broken. For M to infinity this transition approaches that of the one component hard cube gas with fugacity y = zM. We find by direct simulations of such a system a transition at y_c ~ 0.71 which is consistent with the simulation z_c(M) for large M. This transition appears to be always of the Ising type.Comment: 11 pages, 4 postscript figures (added in replacement), Physica A (in press

From the adiabatic piston to macroscopic motion induced by fluctuations

The controversial problem of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated by a piston whose mass is equal to the mass of the fluid particles we obtain a rigorous explicit stationary non-equilibrium solution of the Boltzmann equation. It is shown that at equal pressures on both sides of the piston, the temperature difference induces a non-zero average velocity, oriented toward the region of higher temperature. It thus turns out that despite the absence of macroscopic forces the asymmetry of fluctuations results in a systematic macroscopic motion. This remarkable effect is analogous to the dynamics of stochastic ratchets, where fluctuations conspire with spatial anisotropy to generate direct motion. However, a different mechanism is involved here. The relevance of the discovered motion to the adiabatic piston problem is discussed.Comment: 14 pages,1 figur

The Collective Coordinates Jacobian

We develop an expansion for the Jacobian of the transformation from particle coordinates to collective coordinates. As a demonstration, we use the lowest order of the expansion in conjunction with a variational principle to obtain the Percus Yevick equation for a monodisperse hard sphere system and the Lebowitz equations for a polydisperse hard sphere system.Comment: 7 page