94-188 Aizenman M.

On the slow decay of O(2) correlations in the absence of topological excitations; remark on the Patrascioiu - Seiler model (87K, RTF (Mac)) Jun 6, 94

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Abstract. For spin models with $O(2)$-invariant ferromagnetic interactions, the Patrascioiu-Seiler constraint is: $|\arg (S(x))-\arg (S(y))|\le \theta _o$ for all $|x-y|=1$. It is shown that in two dimensional systems of two-component spins the imposition of such constraints with $\theta _o$ 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 is found to obey: $<S(x)^.S(y)>\,\;\ge \;{3 \over {4|x-y|^2}}$ , at any temperature - including $T=\inf$. The derivation is along the lines proposed by A. Patrascioiu and E. Seiler [1], with the yet unproven conjectures invoked there replaced by another geometric argument. Dedicated to Oliver Penrose on the occasion of his sixty-fifth's birthday. The article is archived in the RTF format. If you would rather have a hard copy, send a request to: aizenman@math.princeton.edu or: M. Aizenman, Jadwin Hall, P.O.Box 708, Princeton, NY 08544- 0708.

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