Percolation and the hard-core lattice gas model

Percolation Games, Probabilistic Cellular Automata, and the Hard-core Model

Let each site of the square lattice Z be independently declared closed with probability p, and otherwise open. Consider the following game: a token starts at the origin, and the two players take turns to move it from its current site x to an open site in {x + (0, 1), x + (1, 0)}; if both these sites are closed, then the player to move loses the game. Is there positive probability that the game ...

Analyticity of a Hard-Core Multicomponent Lattice Gas

A multicompotlent "anti-Widom-Rowlinson" lattice gas is introduced. An arbitrary number M of particle types is permitted, all having the same activity. The only interactions are nearest-neighbor exclusions of like particles (analogous to map-coloring problems). For any lattice it is shown that there is a finite number M0 (depending onty on the coordination number of the lattice) such that for a...

Glassy behavior induced by geometrical frustration in a hard-core lattice-gas model

– We introduce a hard-core lattice-gas model on generalized Bethe lattices and investigate analytically and numerically its compaction behavior. If compactified slowly, the system undergoes a first-order crystallization transition. If compactified much faster, the system stays in a meta-stable liquid state and undergoes a glass transition under further compaction. We show that this behavior is ...

Transfer-Matrix Study of Hard-Core Singularity for Hard-Square Lattice Gas

A singularity on the negative fugacity axis of the hard-square lattice gas is investigated in terms of numerical diagonalization of transfer matrices. The location of the singular point z− c and the critical exponent ν are accurately determined by the phenomenological renormalization technique as −0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the...

Three-phase equilibrium in a binary hard-core lattice model.