On the slow decay of O(2) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model

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Abstract

For spin models with O(2)-invariant ferromagnetic interactions, the Patrascioiu-Seiler constraint is |arg(S(x))-arg(S(y))|≤θ0 for all |x-y|=1. It is shown that in two-dimensional systems of two-component spins the imposition of such contraints with θ0 small enough indeed results in the suppression of exponential clustering. More explicitly, it is shown that in such systems on every scale the spin-spin correlation function obeys 〈S(x)·S(y)〉≥1/(2|x-y|2) at any temperature, including T=∞. The derivation is along the lines proposed by A. Patrascioiu and E. Seiler, with the yet unproven conjectures invoked there replaced by another geometric argument.

Original languageEnglish (US)
Pages (from-to)351-359
Number of pages9
JournalJournal of Statistical Physics
Volume77
Issue number1-2
DOIs
StatePublished - Oct 1 1994

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Continuous symmetry
  • Fortuin-Kasteleyn representation
  • Kosterlitz-Thouless transition
  • decay of correlations
  • topological charges

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