Local height probabilities in a composite Andrews-Baxter-Forrester model

TL;DR

This paper investigates the local height probabilities in a composite model derived from the Andrews-Baxter-Forrester model, linking it to conformal field theories and describing its critical behavior and connection to anyonic chains.

Contribution

It introduces a composite height model that connects to conformal field theories and characterizes the critical behavior of associated anyonic chains.

Findings

Critical behavior described by diagonal coset-model and Fateev-Zamolodchikov parafermions

Connection established between height probabilities and conformal field theory characters

Model exhibits two different critical points with distinct conformal descriptions

Abstract

We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two- and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behaviour of the composite height model, the critical behaviour of the anyonic chains is established as well. Depending on the overall sign of the hamiltonian, this critical behaviour is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.