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Surface properties at the Kosterlitz-Thouless transition

Bertrand Berche
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Abstract

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with free and mixed fixed-free boundary conditions. Using a Schwarz-Christoffel conformal mapping, we deduce the exponent eta of the order parameter correlation function and its surface equivalent eta_parallel at the Kosterlitz-Thouless transition temperature. The well known value eta(T_{KT}) = 1/4 is easily recovered even with systems of relatively small sizes, since the shape effects are encoded in the conformal mapping. The exponent associated to the surface correlations is similarly obtained eta_1(T_{KT}) ~= 0.54.

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Bertrand Berche. 2002-08-27. Surface properties at the Kosterlitz-Thouless transition. https://doi.org/10.1016/s0375-9601(02)01167-2

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