Journal of Statistical Physics

, Volume 77, Issue 1–2, pp 351–359 | Cite as

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

  • Michael Aizenman


For spin models withO(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, includingT=∞. 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.

Key Words

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


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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Michael Aizenman
    • 1
  1. 1.Departments of Physics and MathematicsPrinceton UniversityPrinceton

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