Thermodynamics of a lattice gas with linear attractive potential
Abstract
We study the equilibrium thermodynamics of a one-dimensional 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 well-behaved. 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 non-interacting bosons which are placed on known energy levels. The exact solution shows that the system has a liquid-gas 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
- Journal Name:
- Journal of Mathematical Physics
- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
- 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; ONE-DIMENSIONAL 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. https://doi.org/10.1063/1.4904833
Pirjol, Dan, and Schat, Carlos. 2015.
"Thermodynamics of a lattice gas with linear attractive potential". United States. https://doi.org/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 one-dimensional 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 well-behaved. 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 non-interacting bosons which are placed on known energy levels. The exact solution shows that the system has a liquid-gas 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},
url = {https://www.osti.gov/biblio/22403087},
journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 1,
volume = 56,
place = {United States},
year = {Thu Jan 15 00:00:00 EST 2015},
month = {Thu Jan 15 00:00:00 EST 2015}
}