EXACT PHASE-DIAGRAMS FOR THE CONDENSATION OF A KAGOME LATTICE-GAS WITH 3-PARTICLE INTERACTIONS

The condensation of a two-dimensional kagome lattice gas having purely three-particle interactions is first theoretically investigated. The Hamiltonian H(lg) = -epsilon3 SIGMA[i, j, k] n(i)n(j)n(k), where espil on3 > 0 is the strength parameter of the short-range attractive triple t interaction, the sum is taken over all elementary triangles of the k agome lattice, and n(l) = 0, 1 is an idempotent site-occupation number . The method initially involves transforming the lattice-gas model int o a generalized kagome Ising model having both pair and triplet intera ctions as well as a magnetic field. Since the canonical partition func tion of a generalized kagome Ising model is equivalent (aside from kno wn prefactors) to the canonical partition function of a standard honey comb Ising model in a magnetic field, one can deduce the exact liquid- vapor phase diagrams of the triplet-interaction kagome lattice gas fro m its grand canonical partition function. As results, the liquid-vapor phase boundary (reduced chemical potential mu/epsilon3 vs reduced tem perature T/T(c)) is found to be curvilinear with a positive slope, ori ginating at zero temperature with mu/epsilon3 = -2/3 and analytic at i ts terminating critical point whose coordinates are T/T(c) = 1, mu(c)/ epsilon3 = -0.64469 ..., where epsilon3/k(B)T(c) = 3.96992.... The com panion coexistence curve (particle number density rho vs. reduced temp erature T/T(c)) exhibits an asymmetric rounded shape with a positive-s lope curvilinear diameter, and the value of the critical density rho(c ) = 0.58931 .... At criticality, the expression for the coexistence cu rve superposes a pair of branch point singularities resulting in an in finite (vertical) slope at the critical point (T/T(c) = rho/rho(c) = 1 ). The case of a kagome lattice gas having mixed attractive pair inter actions and very weak repulsive triplet interactions (Axilrod-Teller) is next considered. Perturbation analyses upon exact expressions relat ing to the phase diagrams reveal, over chosen ranges of reduced temper atures, that the phase boundary and the diameter of the two-phase coex istence region each have a negative slope due to the repulsive three-p article interactions.