Phase transitions in anisotropic lattice spin systems

Jürg Fröhlich, Elliott Lieb

Research output: Contribution to journalArticle

107 Scopus citations

Abstract

A general method for proving the existence of phase transitions is presented and applied to six nearest neighbor models, both classical and quantum mechanical, on the two dimensional square lattice. Included are some two dimensional Heisenberg models. All models are anisotropic in the sense that the groundstate is only finitely degenerate. Using our method which combines a Peierls argument with reflection positivity, i.e. chessboard estimates, and the principle of exponential localization we show that five of them have long range order at sufficiently low temperature. A possible exception is the quantum mechanical, anisotropic Heisenberg ferromagnet for which reflection positivity is not proved, but for which the rest of the proof is valid.

Original languageEnglish (US)
Pages (from-to)233-267
Number of pages35
JournalCommunications in Mathematical Physics
Volume60
Issue number3
DOIs
StatePublished - Oct 1 1978

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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