A refinement of Simon's correlation inequality

Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


A general formulation is given of Simon's Ising model inequality: {Mathematical expression} where B is any set of spins separating α from γ. We show that 〈σbσα〉 can be replaced by 〈σbσαA where A is the spin system "inside"B containing α. An advantage of this is that a finite algorithm can be given to compute the transition temperature to any desired accuracy. The analogous inequality for plane rotors is shown to hold if a certain conjecture can be proved. This conjecture is indeed verified in the simplest case, and leads to an upper bound on the critical temperature. (The conjecture has been proved in general by Rivasseau. See notes added in proof.)

Original languageEnglish (US)
Pages (from-to)127-135
Number of pages9
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - Oct 1980

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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