Journal of Statistical Physics. Vol. 77, Nos. 1/2. 1994, p. 351-359.
For spin models with O(2)-invariant ferromagnetic interactions, the Patrascioiu-Seiler constraint is |arg(S(x))-arg(S(y))| \< teta_0 for all |x-y| = 1. It is shown that in two-dimensional systems of two-component spins the imposition of such constraints with teta_0 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 f~nction obeys (S(x)*S(y)) >/ 1/(2|x- y|^2) at any temperature, including T= oo. 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.