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))

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.