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  • Letter
  • Open Access

Finite-size corrections to the crosscap overlap in the two-dimensional Ising model

Yiteng Zhang1,*, Li-Ping Yang2,†, Hong-Hao Tu3,‡, and Yueshui Zhang1,3,§

  • *Contact author: z.yt-wangzai@connect.hku.hk
  • †Contact author: liping2012@cqu.edu.cn
  • ‡Contact author: h.tu@lmu.de
  • §Contact author: yueshui@hku.hk
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Phys. Rev. E 114, L042110 – Published 27 October, 2026

DOI: https://doi.org/10.1103/dcvm-ddc5

Abstract

We analyze the finite-size corrections to the crosscap overlap in the two-dimensional classical Ising model along its self-dual critical line. Using a fermionic formulation, we express the lattice crosscap overlap in terms of Bogoliubov angles and develop a contour-integral approach by analytically continuing the lattice momentum to the complex plane. This leads to a remarkably simple expression for the crosscap overlap, which demonstrates that the finite-size corrections decay exponentially with system size. We further derive an exact analytical formula for the corresponding decay constant and show that it is determined by the complex singularity structure of the Bogoliubov angle.

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Outline

Information

Phys. Rev. E 114, L042110– Published 27 October, 2026
  • Received 3 February 2026
  • Revised 27 August 2026
  • Accepted 14 October 2026
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