Lattice systems with a continuous symmetry - III. Low temperature asymptotic expansion for the plane rotator model

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

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures for d=3.

Original languageEnglish (US)
Pages (from-to)545-566
Number of pages22
JournalCommunications in Mathematical Physics
Volume78
Issue number4
DOIs
StatePublished - Jan 1 1981

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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