Local Ward identities and the decay of correlations in ferromagnets

Michael Aizenman, Barry Simon

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Using local Ward identities we prove a number of correlation inequalities for N-component, isotropically coupled, pair interacting ferromagnets; some for all N≧2 and some for N=2, 3, 4. These are used to prove a mass gap above the mean field temperature, for all N≧2. For N=2, 3, 4 we prove an upper bound on a critical exponent, and a lower bound on the susceptability which diverges as m→0.

Original languageEnglish (US)
Pages (from-to)137-143
Number of pages7
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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