Exact coexistence-curve diameter of a lattice gas with pair and triplet interactions

1989 ◽  
Vol 63 (4) ◽  
pp. 465-465 ◽  
Author(s):  
F. Y. Wu ◽  
X. N. Wu
Keyword(s):  
Lattice Gas ◽  
Coexistence Curve ◽  
Pair And Triplet Interactions

EXACT PHASE DIAGRAMS FOR THE CONDENSATION OF A KAGOMÉ LATTICE GAS WITH THREE-PARTICLE INTERACTIONS

1993 ◽  
Vol 07 (15) ◽  
pp. 2831-2857 ◽  
Author(s):  
J.H. BARRY ◽  
N.S. SULLIVAN
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Phase Diagrams ◽  
Lattice Gas ◽  
Coexistence Curve ◽  
Particle Interactions ◽  
Kagome Lattice ◽  
Canonical Partition Function ◽  
Kagomé Lattice ◽  
Reduced Temperature

The condensation of a two-dimensional kagomé lattice gas having purely three-particle interactions is first theoretically investigated. The Hamiltonian Hℓg=−∈3Σ<i, j, k> ninjnk, where ∈3>0 is the strength. parameter of the short-range attractive triplet interaction, the sum is taken over all elementary triangles of the kagomé lattice, and nℓ=0, 1 is an idempotent site-occupation number. The method initially involves transforming the lattice-gas model into a generalized kagomé Ising model having both pair and triplet interactions as well as a magnetic field. Since the canonical partition function of a generalized kagomé Ising model is equivalent (aside from known prefactors) to the canonical partition function of a standard honeycomb Ising model in a magnetic field, one can deduce the exact liquid-vapor phase diagrams of the triplet-interaction kagomé lattice gas from its grand canonical partition function. As results, the liquid-vapor phase boundary (reduced chemical potential μ/∈3 vs reduced temperature T/Tc) is found to be curvilinear with a positive slope, originating at zero temperature with μ/∈3=−2/3 and analytic at its terminating critical point whose coordinates are T/Tc=1, μc/∈3=−0.64469…, where ∈3/kBTc=3.96992…. The companion coexistence curve (particle number density ρ vs. reduced temperature T/Tc) exhibits an asymmetric rounded shape with a positive-slope curvilinear diameter, and the value of the critical density ρc=0.58931…. At criticality, the expression for the coexistence curve superposes a pair of branch point singularities resulting in an infinite (vertical) slope at the critical point (T/Tc=ρ/ρc=1). The case of a kagomé lattice gas having mixed attractive pair interactions and very weak repulsive triplet interactions (Axilrod-Teller) is next considered. Perturbation analyses upon exact expressions relating to the phase diagrams reveal, over chosen ranges of reduced temperatures, that the phase boundary and the diameter of the two-phase coexistence region each have a negative slope due to the repulsive three-particle interactions.

Coexistence curve properties of Mermin's decorated lattice gas

1974 ◽  
Vol 60 (4) ◽  
pp. 1297-1306 ◽  
Author(s):  
G. W. Mulholland ◽  
J. J. Rehr
Keyword(s):  
Lattice Gas ◽  
Coexistence Curve

HOPPING AND STATIC CORRELATIONS OF HIGHER ORDER IN A LATTICE GAS

1985 ◽  
Vol 46 (C9) ◽  
pp. C9-141-C9-143 ◽  
Author(s):  
K. Froböse ◽  
J. Jäckle
Keyword(s):  
Lattice Gas ◽  
Higher Order

Counting Lattice-Gas Invariants

1993 ◽  
Author(s):  
Jeffrey Yepez
Keyword(s):  
Lattice Gas
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