Order Parameters of the Dilute A Models

TL;DR

This paper analytically calculates the free energy and local height probabilities of dilute A models, revealing their critical behavior, conformal weights, and connection to the Ising model in a magnetic field.

Contribution

It provides new analytical results for dilute A models with broken symmetry, including their critical exponents and relation to minimal and Ising models.

Findings

Identified four critical branches of dilute A models.

Derived critical exponents and conformal weights from order parameters.

Showed dilute A₃ model's universality class as the Ising model in a magnetic field.

Abstract

The free energy and local height probabilities of the dilute A models with broken $\Integer_2$ symmetry are calculated analytically using inversion and corner transfer matrix methods. These models possess four critical branches. The first two branches provide new realisations of the unitary minimal series and the other two branches give a direct product of this series with an Ising model. We identify the integrable perturbations which move the dilute A models away from the critical limit. Generalised order parameters are defined and their critical exponents extracted. The associated conformal weights are found to occur on the diagonal of the relevant Kac table. In an appropriate regime the dilute A$_3$ model lies in the universality class of the Ising model in a magnetic field. In this case we obtain the magnetic exponent $\delta=15$ directly, without the use of scaling relations.