Thermodynamics of a lattice gas with linear attractive potential
Abstract
We study the equilibrium thermodynamics of a onedimensional lattice gas with interaction V(i−j)=−1/(μn) (ξ−1/n i−j) given by the superposition of a universal attractive interaction with strength −1/(μn) ξ<0, and a linear attractive potential 1/(μn{sup 2}) i−j. The interaction is rescaled with the lattice size n, such that the thermodynamical limit n → ∞ is wellbehaved. The thermodynamical properties of the system can be found exactly, both for a finite size lattice and in the thermodynamical limit n → ∞. The lattice gas can be mapped to a system of noninteracting bosons which are placed on known energy levels. The exact solution shows that the system has a liquidgas phase transition for ξ > 0. In the large temperature limit T ≫ T{sub 0}(ρ) = ρ{sup 2}/(4μ) with ρ the density, the system becomes spatially homogeneous, and the equation of state is given to a good approximation by a lattice version of the van der Waals equation, with critical temperature T{sub c}{sup (vdW)}=1/(12μ) (3ξ−1)
 Authors:
 Department of Particle Physics, National Institute for Physics and Nuclear Engineering, 077125 Bucharest (Romania)
 Departamento de Física, FCEyN, Universidad de Buenos Aires and IFIBA, CONICET, Ciudad Universitaria, Pab. 1, 1428 Buenos Aires (Argentina)
 Publication Date:
 OSTI Identifier:
 22403087
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CRITICAL TEMPERATURE; EQUATIONS OF STATE; EQUILIBRIUM; EXACT SOLUTIONS; INTERACTING BOSON MODEL; INTERACTIONS; ONEDIMENSIONAL CALCULATIONS; PHASE TRANSFORMATIONS; POTENTIALS; THERMODYNAMICS
Citation Formats
Pirjol, Dan, and Schat, Carlos. Thermodynamics of a lattice gas with linear attractive potential. United States: N. p., 2015.
Web. doi:10.1063/1.4904833.
Pirjol, Dan, & Schat, Carlos. Thermodynamics of a lattice gas with linear attractive potential. United States. doi:10.1063/1.4904833.
Pirjol, Dan, and Schat, Carlos. 2015.
"Thermodynamics of a lattice gas with linear attractive potential". United States.
doi:10.1063/1.4904833.
@article{osti_22403087,
title = {Thermodynamics of a lattice gas with linear attractive potential},
author = {Pirjol, Dan and Schat, Carlos},
abstractNote = {We study the equilibrium thermodynamics of a onedimensional lattice gas with interaction V(i−j)=−1/(μn) (ξ−1/n i−j) given by the superposition of a universal attractive interaction with strength −1/(μn) ξ<0, and a linear attractive potential 1/(μn{sup 2}) i−j. The interaction is rescaled with the lattice size n, such that the thermodynamical limit n → ∞ is wellbehaved. The thermodynamical properties of the system can be found exactly, both for a finite size lattice and in the thermodynamical limit n → ∞. The lattice gas can be mapped to a system of noninteracting bosons which are placed on known energy levels. The exact solution shows that the system has a liquidgas phase transition for ξ > 0. In the large temperature limit T ≫ T{sub 0}(ρ) = ρ{sup 2}/(4μ) with ρ the density, the system becomes spatially homogeneous, and the equation of state is given to a good approximation by a lattice version of the van der Waals equation, with critical temperature T{sub c}{sup (vdW)}=1/(12μ) (3ξ−1)},
doi = {10.1063/1.4904833},
journal = {Journal of Mathematical Physics},
number = 1,
volume = 56,
place = {United States},
year = 2015,
month = 1
}

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