Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 216-06. BKT universality for height and planar spin fields
Manuscript map · lines 6375–6384
OpenAI@2026-10-07#rem:oai-p-216-06
Authors: OpenAI. Family 216.
Title: BKT universality for height and planar spin fields.
Abstract: We prove Gaussian scaling limits for the two-dimensional discrete Gaussian height model throughout its rough phase, including the physical roughening threshold, for every finite square-symmetric interaction set containing the nearest neighbors. After the natural lattice normalization, the critical effective temperature has the universal value $8{}pi$. For the ordinary nearest-neighbor Villain and XY models at sufficiently low fixed temperatures, we also prove that their Green-function-normalized spin fields converge to the imaginary exponential of a Dirichlet Gaussian free field.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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