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

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.