Thermodynamic properties of lattice hard-sphere models

Abstract

Thermodynamic properties of several lattice hard-sphere models were obtained from grand canonical histogram- reweighting Monte Carlo simulations. Sphere centers occupy positions on a simple cubic lattice of unit spacing and exclude neighboring sites up to a distance sigma. The nearestneighbor exclusion model, sigma = radical2, was previously found to have a second-order transition. Models with integer values of sigma = 1 or 2 do not have any transitions. Models with sigma = radical3 and sigma = 3 have weak first-order fluid-solid transitions while those with sigma = 2 radical2, 2 radical3, and 3 radical2 have strong fluid-solid transitions. Pressure, chemical potential, and density are reported for all models and compared to the results for the continuum, theoretical predictions, and prior simulations when available.

Monte Carlo simulations of two-dimensional hard core lattice gases

“…Note that the maximum density is 1/2. In higher dimensions [24,30,31,54,55,56,57,58] and other geometries (see [40] and references therein), the same kind of transition is observed, also belonging to the Ising universality class.…”

“…Interestingly, no transition was found for the analogous d = 3 system of hard-cubes with λ = 2 [58] on a cubic lattice. On the other hand, nearest and next nearest neighbors exclusion in d = 3 presents a weak first order transition [58]. Other lattices have also been considered, see Refs.…”

“…The close packed configuration, like in the 2NN (λ = 2) case, is not uniquely defined and has a density ρ MAX = 1/9. In d = 3, this system undergoes a weak first order phase transition as density increases [58], although there seems to be no information concerning the d = 2 case. The corresponding sublattice division is analogous to the 2NN case, only that now nine sublattices are necessary, the order parameter being…”

Critical Casimir interactions and colloidal self-assembly in near-critical solvents

“…44 Our model also derives inspiration from the "finely discretized" lattice model of Panagiotopoulos. 45,46 To elaborate, colloids C are discretized hard disks (HD) with a radius R, measured in number of lattice sites, and occupy a set of sites S C = {r i | d(r i ,r C ) ≤ R}, where r C are the lattice coordinates of the disk, r i are the coordinates of lattice site i, and the function d(a, b) calculates the absolute distance between a and b using the minimum image convention. The disks have only translational degrees of freedom, and their Hamiltonian H C (in the absence of the solvent mixture) is zero for non-overlapping configurations, and is infinite if any pair of colloids overlap, or if a colloid and solvent site overlap.…”

Phase transitions of a lattice model for patchy particles with tetrahedral symmetry

“…The use of lattice models has proven to be very fruitful [18][19][20][21][22][23][24][25][26][27][28] in the analysis of the phase diagram of simple models with complex phase behaviour, with the advantage that simulations can be performed for larger system sizes with higher accuracy. For example, it has been shown that it is possible to design associating lattice models that reproduce some of the behaviour of water, including the density and diffusion anomalies [22,27,28].…”