## 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≤0.77β_{critical}.

Original language | English (US) |
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Pages (from-to) | 195-220 |

Number of pages | 26 |

Journal | Journal of Statistical Physics |

Volume | 59 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 1990 |

## Keywords

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

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics