Critical behaviour of the discrete spin cubic model

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52 Scopus citations

Abstract

An n-component spin model, with the nearest-neighbour Hamiltonian H=-J Sigma (Si.Sj)-K Sigma (Si.Sj) 2, where Si is a discrete unit vector pointing only along one of the 2n cubic axes directions, is studied exactly at dimensions d=1 and d=1+ epsilon and approximately (using dedecoration renormalization group recursion relations) at d=2. The model exhibits four competing possible types of critical behaviour, related to the Ising model, to the n-state and 2n-state Potts models and to a 'new cubic' fixed point. For large n, at d=2, the last three types of behaviour show peculiarities which may be related to the transition becoming a first-order one.

Original languageEnglish
Article number011
Pages (from-to)389-398
Number of pages10
JournalJournal of Physics A: General Physics
Volume10
Issue number3
DOIs
StatePublished - 1 Dec 1977
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics

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