- 98-500 Chayes L.
- Discontinuity of the Spin--Wave Stiffness in the two--dimensional XY Model
Jul 10, 98
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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