Phase transition in zero dimensions: A remark on the spherical model

Elliott H. Lieb, Colin J. Thompson

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

It is shown that the spherical model consisting of N spins with nonzero interaction between two spins only has a phase transition in the limit N → ∞. This is a counterexample to a suggestion of Kac which states that an Ising model will have a transition if the corresponding spherical model has a transition. Possible modifications of Kac's conjecture are suggested and discussed.

Original languageEnglish (US)
Pages (from-to)1403-1406
Number of pages4
JournalJournal of Mathematical Physics
Volume10
Issue number8
DOIs
StatePublished - Jan 1 1969

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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