Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 216-01. The critical logarithmic correction for the planar XY model
Manuscript map · lines 6325–6334
OpenAI@2026-10-07#rem:oai-p-216-01
Authors: OpenAI. Family 216.
Title: The critical logarithmic correction for the planar XY model.
Abstract: We prove the critical logarithmic correction for the nearest-neighbor cosine XY model on the square lattice. Let $C_{b_c}(r)$ be the two-point correlation at critical inverse temperature, obtained by taking the free-box thermodynamic limit while the two sites remain r lattice steps apart along a coordinate axis. Then ${}displaystyle C_{b_c}(r)=B_{{}mathrm{XY}}r{}{-1/4}({}log r){}{1/8}(1+o(1)), {}qquad B_{{}mathrm{XY}}{}in(0,{}infty),$ as $r{}to{}infty$.
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.
Nearby in this section
- section: Manuscript map
- remark: Remark: 001-01. Milne's rationality conjecture for abelian varieties
- remark: Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
- remark: Remark: 002-02. The Selmer converse for elliptic curves at every prime
- remark: Remark: 002-03. The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one
- remark: Remark: 003-01. The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane s 7/8
- remark: Remark: 003-02. The Quasi-Riemann Hypothesis (alternate 11/12 proof)
- remark: Remark: 003-03. Uniform exclusion of Landau–Siegel zeros