Approximation of Cluster Integrals for Various Lattice-Gas Models

  • S. Yu. Ushcats Admiral Makarov National University of Shipbuilding
  • M. V. Ushcats Admiral Makarov National University of Shipbuilding, Taras Shevchenko National University of Kyiv, Faculty of Physics
  • V. M. Sysoev Taras Shevchenko National University of Kyiv, Faculty of Physics
  • D. A. Gavryushenko Taras Shevchenko National University of Kyiv, Faculty of Physics
Keywords: lattice gas, virial series, cluster integral, hole-particle symmetry, convergence radius, saturation point, boiling point

Abstract

An approximation for cluster integrals of an arbitrary high order has been proposed for the well-known lattice-gas model with an arbitrary geometry and dimensions. The approximation is based on the recently obtained accurate relations for the convergence radius of the virial power series in the activity parameter for the pressure and density. As compared to the previous studies of the symmetric virial expansions for the gaseous and condensed states of a lattice gas, the proposed approximation substantially approaches the pressure values at the saturation and boiling points. For the Lee–Yang lattice-gas model, the approximation considerably improves the convergence to the known exact solution.

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Published
2018-12-09
How to Cite
Ushcats, S., Ushcats, M., Sysoev, V., & Gavryushenko, D. (2018). Approximation of Cluster Integrals for Various Lattice-Gas Models. Ukrainian Journal of Physics, 63(12), 1066. https://doi.org/10.15407/ujpe63.12.1066
Section
Physics of liquids and liquid systems, biophysics and medical physics