The crossing multiplier for solvable lattice models

TL;DR

This paper derives a general formula for crossing multipliers in solvable lattice models based on conformal field theory, linking them to characters of the underlying theories, and explores their implications for local state probabilities.

Contribution

It provides a unified formula for crossing multipliers in a broad class of solvable lattice models derived from conformal field theories.

Findings

Crossing multipliers are given by the specialized characters of the associated conformal field theory.

A conjecture that crossing multipliers universally correspond to conformal characters in these models.

Local state probabilities are described by the branching rules in regime III.

Abstract

We study the large class of solvable lattice models, based on the data of conformal field theory. These models are constructed from any conformal field theory. We consider the lattice models based on affine algebras described by Jimbo et al., for the algebras $ABCD$ and by Kuniba et al. for $G_2$. We find a general formula for the crossing multipliers of these models. It is shown that these crossing multipliers are also given by the principally specialized characters of the model in question. Therefore we conjecture that the crossing multipliers in this large class of solvable interaction round the face lattice models are given by the characters of the conformal field theory on which they are based. We use this result to study the local state probabilities of these models and show that they are given by the branching rule, in regime III.