In a strictly short-range XY model made of a plane intersected by parallel planes, true long-range order appears along the intersection lines when the parallel planes enter a Berezinskii-Kosterlitz-Thouless critical phase.
Bulk and surface properties in the critical phase of the two-dimensional XY model
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abstract
Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with various boundary conditions (BC). Using conformal mappings we deduce the exponent $\eta_\sigma(T)$ of the order parameter correlation function and its surface analogue $\eta_\|(T)$ as a function of the temperature in the critical (low-temperature) phase of the model.
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Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter
In a strictly short-range XY model made of a plane intersected by parallel planes, true long-range order appears along the intersection lines when the parallel planes enter a Berezinskii-Kosterlitz-Thouless critical phase.