Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 216-04. Essential Singularity of the Correlation Length in the Planar XY Model
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OpenAI@2026-10-07#rem:oai-p-216-04
Authors: OpenAI. Family 216.
Title: Essential Singularity of the Correlation Length in the Planar XY Model.
Abstract: We prove the Berezinskii–Kosterlitz–Thouless essential singularity for the correlation length of the nearest-neighbor cosine XY model on the square lattice. Let $m(b)$ be the mass obtained by taking first the free-box thermodynamic limit and then the separation limit along a coordinate axis. As the inverse temperature b approaches bc from the massive side, ${}displaystyle {}sqrt{b_c-b}{}log{}frac{1}{m(b)} {}longrightarrow A_{{}mathrm{XY}},$ where $A_{{}mathrm{XY}}$ is a finite, strictly positive model-specific constant.
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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