 94188 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 PatrascioiuSeiler constraint is:
$\arg (S(x))\arg (S(y))\le \theta _o$
for all $xy=1$. It is shown that in two dimensional systems of
twocomponent 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
spinspin correlation function is found to obey:
$<S(x)^.S(y)>\,\;\ge \;{3 \over {4xy^2}}$ ,
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 sixtyfifth'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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