Lattice systems with a continuous symmetry - I. Perturbation theory for unbounded spins

Jean Bricmont, Jean Raymond Fontaine, Joel L. Lebowitz, Thomas Spencer

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We investigate a continuous Ising system on a lattice, equivalently an anharmonic crystal, with interactions: {Mathematical expression} We prove that the perturbation expansion for the free energy and for the correlation functions is asymptotic about λ=0, despite the fact that the reference system (λ=0) does not cluster exponentially. The results can be extended to more general systems of this type, e.g. an even polynomial semibounded from below instead of a quartic interaction. By a suitable scaling, λ corresponds to the temperature.

Original languageEnglish (US)
Pages (from-to)281-302
Number of pages22
JournalCommunications In Mathematical Physics
Volume78
Issue number2
DOIs
StatePublished - Dec 1980

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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