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Density functional theory for general hard-core lattice gases.

Luis Lafuente1, José A Cuesta

  • 1Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Madrid, Spain. llafuent@math.uc3m.es

Physical Review Letters
|November 5, 2004
PubMed
Summary

We developed a simple method to approximate free-energy density functionals for hard-core lattice gases. This approach works for various particle shapes, lattices, and dimensions, offering a versatile tool for statistical mechanics.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Physical Chemistry

Background:

  • Hard-core lattice gases are fundamental models in statistical mechanics.
  • Developing accurate free-energy functionals is crucial for understanding phase behavior.
  • Existing methods often lack generality across different system parameters.

Purpose of the Study:

  • To present a general procedure for approximating free-energy density functionals.
  • To develop functionals applicable to any hard-core lattice gas.
  • To ensure consistency through dimensional reduction.

Main Methods:

  • A conceptually simple, general procedure is proposed.
  • The method yields fundamental measure density functionals.
  • Consistency through dimensional reduction is inherent.

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Main Results:

  • An approximate free-energy density functional is obtained for diverse hard-core lattice gases.
  • The procedure recovers known results for specific systems.
  • The derived functionals are consistent across dimensions.

Conclusions:

  • The proposed method offers a unified approach to hard-core lattice gas free-energy calculations.
  • The fundamental measure functionals provide a robust theoretical framework.
  • Potential extensions to attractive lattice models are discussed.