Finitized Conformal Spectra of the Ising Model on the Klein Bottle and Moebius Strip

TL;DR

This paper analyzes the conformal spectra of the critical Ising model on Klein bottle and M"obius strip topologies using Yang-Baxter techniques, deriving finitized partition functions and confirming eigenvalue properties numerically.

Contribution

It introduces a method to compute finitized conformal partition functions for the Ising model on non-trivial topologies using Yang-Baxter and functional equations.

Findings

Derived explicit finitized conformal partition functions.

Confirmed eigenvalue properties numerically.

Extended techniques to non-orientable surfaces.

Abstract

We study the conformal spectra of the critical square lattice Ising model on the Klein bottle and M\"obius strip using Yang-Baxter techniques and the solution of functional equations. In particular, we obtain expressions for the finitized conformal partition functions in terms of finitized Virasoro characters. This demonstrates that Yang-Baxter techniques and functional equations can be used to study the conformal spectra of more general exactly solvable lattice models in these topologies. The results rely on certain properties of the eigenvalues which are confirmed numerically.