Chayes L.
Discontinuity of the Spin--Wave Stiffness in the two--dimensional XY Model
(60K, amstex)

ABSTRACT.  Using a graphical representation based on the Wolff algorithm,the
(classical) $d$--dimensional $XY$ model and some
related spin--systems are studied.
It is proved that in $d=2$, the predicted
discontinuity in the spin--wave stiffness indeed occurs.
Further, the critical properties of the spin--system are
related to percolation properties of the graphical
representation.  In particular, a suitably defined notion of
percolation in the graphical representation  is proved to be
the necessary and sufficient condition for positivity  of the
spontaneous magnetization.