Multicomponent field theories and classical rotators

François Dunlop, Charles M. Newman

Research output: Contribution to journalArticle

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

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Field Theory
Euclidean
theorems
Heisenberg Model
Quantum Fields
Theorem
Transverse
Valid
Interaction
Model
interactions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Multicomponent field theories and classical rotators. / Dunlop, François; Newman, Charles M.

In: Communications in Mathematical Physics, Vol. 44, No. 3, 10.1975, p. 223-235.

Research output: Contribution to journalArticle

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