Journal of Statistical Physics

, Volume 59, Issue 1–2, pp 195–220 | Cite as

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

  • Tom Kennedy


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 forβ⩽0.77βcritical.

Key words

Finite volume condition high temperature phase lattice spin system 


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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Tom Kennedy
    • 1
  1. 1.Department of MathematicsUniversity of ArizonaTucson

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