The boundary disorder correlation for the Ising model on a cylinder

TL;DR

This paper derives an explicit formula for the correlation function of disorder insertions in the critical Ising model on a cylinder, linking it to finite size scaling and Jacobi theta functions, enhancing understanding of boundary effects.

Contribution

It provides a new exact expression for disorder correlation functions on a cylinder, connecting boundary conditions, aspect ratio, and finite size scaling in the Ising model.

Findings

Explicit correlation function formula derived

Connection between boundary conditions and finite size effects established

Expression involves Jacobi theta functions

Abstract

I give an expression for the correlation function of disorder insertions on the edges of the critical Ising model on a cylinder as a function of the aspect ratio (rescaled in the case of anisotropic couplings). This is obtained from an expression for the finite size scaling term in the free energy on a cylinder in periodic and antiperiodic boundary conditions in terms of Jacobi theta functions.