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

TL;DR

This paper derives an exact analytical expression for finite-size corrections to the crosscap overlap in the 2D Ising model, showing exponential decay governed by complex singularities, using a fermionic and contour integral approach.

Contribution

It introduces a novel contour-integral method to compute finite-size corrections in the Ising model's crosscap overlap, linking decay constants to singularity structures.

Findings

Finite-size corrections decay exponentially with system size.

Derived an exact formula for the decay constant.

Connected decay behavior to complex singularities of Bogoliubov angles.

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.