98-500 Chayes L.

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

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