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Asymptotic free energy of a system with periodic boundary conditions

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Abstract

A ν-dimensional classical particle system in a torus, i.e., in a rectangular box with periodic boundary conditions, is considered in a canonical ensemble. Subject to mild restrictions over and above the usual stability and tempering conditions it is proved that the thermodynamic limit for the torus exists and is identical with that for systems contained in normal domains with boundaries or walls. If, in addition, the pair interaction potential ϕ(r) decreases sufficiently rapidly (so thatr∣ϕ(r)∣ is integrable at ∞), and satisfies some further regularity conditions, then the difference between the free energies of the torus and of the corresponding box is at most of the order of a surface term. Somewhat stronger results are indicated for the grand canonical pressure.

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References

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Authors and Affiliations

  1. Baker Laboratory, Cornell University, Ithaca, New York

    Michael E. Fisher

  2. Belfer Graduate School of Science, New York, New York

    J. L. Lebowitz

Authors
  1. Michael E. Fisher
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  2. J. L. Lebowitz
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Fisher, M.E., Lebowitz, J.L. Asymptotic free energy of a system with periodic boundary conditions. Commun.Math. Phys. 19, 251–272 (1970). https://doi.org/10.1007/BF01646633

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  • DOI: https://doi.org/10.1007/BF01646633

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