Bose-Einstein condensation in an exactly soluble system of interacting particles

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The model investigated recently by Tóth, a lattice gas of bosons with hard-core repulsion on a complete graph, is studied here by diagonalizing the Hamiltonian. The thermodynamic free energy per site is shown to be f, where {Mathematical expression} where ß is the inverse temperature and ??[0, 1] is the number of particles per site. This formula is equivalent to the one obtained by Tóth. There is a phase transition at ß +ß* (?) = (1-2 ?)-1 log[(1-?)/?]. If ß=ß*(?), Bose-Einstein condensation is shown to be present, the condensate density (number of condensed particles per site) in the thermodynamic limit being [?-x*][l-?-x*], where x* is the minimizing value of x, satisfying ß*(x*)=ß. © 1991 Plenum Publishing Corporation.

Original languageEnglish
Pages (from-to)761-781
Number of pages21
JournalJournal of Statistical Physics
Issue number3-4
Publication statusPublished - May 1991


  • Bose-Einstein condensation
  • mean-field theories
  • quantum lattice gas
  • XY model


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