PDE and mathematical physics · Oct 6, 2026
Critical and near-critical XY scaling and BKT universality
For the square-lattice nearest-neighbor cosine XY model, proves critical axis correlations and the Berezinskii–Kosterlitz–Thouless essential singularity , with after the free-box thermodynamic limit. For finite square-symmetric interactions containing nearest neighbors, discrete Gaussian heights converge to Gaussian fields throughout the rough phase, including its threshold, along geometric torus sizes. Critical center-magnetization and spin-field conclusions retain their stated height, renormalization, and field-input assumptions.
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