Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 216-03. The Critical Spin Field of the Planar XY Model
Manuscript map · lines 6345–6354
OpenAI@2026-10-07#rem:oai-p-216-03
Authors: OpenAI. Family 216.
Title: The Critical Spin Field of the Planar XY Model.
Abstract: Using the companion critical Bessel-height and pin-limit theorems, we prove that at the mass-defined critical inverse temperature of the nearest-neighbor XY model on the square lattice, the spin field on a square with boundary angles fixed to zero converges along the full sequence to the full-variance imaginary exponential of a zero-Dirichlet Gaussian free field with stiffness $2/{}pi$. The normalization uses the exact center magnetization and the lattice Green-function factor. Convergence holds in law in $H{}{-3}_{{}mathrm{loc}}((-1,1){}2)$; all mixed moments and joint laws of fields smeared against smooth compactly supported test functions in $(-1,1){}2$ converge as well.
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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