Multicomponent field theories and classical rotators

François Dunlop, Charles M. Newman

Research output: Contribution to journalArticlepeer-review

Abstract

It is shown that a D-component Euclidean quantum field, φ{symbol}=(φ{symbol}1,...,φ{symbol}D), with λ|φ{symbol}|4+β|φ{symbol}2| interaction, can be obtained as a limit of (ferromagnetic) classical rotator models; this extends a result of Simon and Griffiths from the case D=1. For these Euclidean field models, it is then shown that a Lee-Yang theorem applies for D=2 or 3 and that Griffiths' second inequality is valid for D=2; a complete proof is included of a Lee-Yang theorem for plane rotator and classical Heisenberg models. As an application of Griffiths' second inequality for D=2, an interesting relation between the "parallel" and "transverse" two-point correlations is obtained.

Original languageEnglish (US)
Pages (from-to)223-235
Number of pages13
JournalCommunications In Mathematical Physics
Volume44
Issue number3
DOIs
StatePublished - Oct 1975

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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