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

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.

💡 Research Summary

In this work the authors investigate finite‑size effects in the overlap between the ground state of the two‑dimensional classical Ising model and a lattice crosscap state, focusing on the self‑dual critical line where the model is described by the c = ½ Ising conformal field theory. By mapping the classical model to a transfer‑matrix formalism and exploiting its equivalence to an anisotropic quantum XY chain, they diagonalize the transfer matrix using a Jordan‑Wigner transformation followed by a Fourier transform and a Bogoliubov rotation. The Bogoliubov angle θ(k)=arctan