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Discontinuity of the Spin-Wave Stiffness in the Two-Dimensional XY Model

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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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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA.¶E-mail: lchayes@math.ucla.edu, , , , , , US

    L. Chayes

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  1. L. Chayes
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Received: 21 March 1997 / Accepted: 3 March 1998

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Chayes, L. Discontinuity of the Spin-Wave Stiffness in the Two-Dimensional XY Model. Comm Math Phys 197, 623–640 (1998). https://doi.org/10.1007/s002200050466

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  • DOI: https://doi.org/10.1007/s002200050466

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