A fixed-point equation for the high-temperature phase of discrete lattice spin systems

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Abstract

A fixed-point equation on an infinite-dimensional space is proposed as an alternative to the usual definition of the infinite-volume limit in discrete lattice spin systems in the high-temperature phase. It is argued heuristically that the free energy and correlation functions one obtains by solving this equation agree with the usual definitions of these quantities. A theorem is then proved that says that if a certain finite-volume condition is satisfied, then this fixed-point equation has a solution and the resulting free energy is analytic in the parameters in the Hamiltonian. For particular values of the temperature this finite-volume condition may be checked with the help of a computer. The two-dimensional Ising model is considered as a test case, and it is shown that the finite-volume condition is satisfied for β≤0.77βcritical.

Original languageEnglish (US)
Pages (from-to)195-220
Number of pages26
JournalJournal of Statistical Physics
Volume59
Issue number1-2
DOIs
StatePublished - Apr 1 1990

Keywords

  • Finite volume condition
  • high temperature phase
  • lattice spin system

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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