The dilute A$_4$ model, the E$_7$ mass spectrum and the tricritical Ising model

TL;DR

This paper uses exact perturbation methods to derive correlation lengths and mass spectra of the dilute A4 lattice model, linking it to the tricritical Ising model and E7 scattering theory.

Contribution

It provides the first derivation of mass gaps and correlation lengths for the dilute A4 model from Bethe ansatz, connecting lattice models to conformal field theory and scattering predictions.

Findings

Derived seven elementary correlation lengths and mass gaps.

Connected the dilute A4 model to E7 mass spectrum.

Calculated universal amplitudes for the tricritical Ising model.

Abstract

The exact perturbation approach is used to derive the (seven) elementary correlation lengths and related mass gaps of the two-dimensional dilute A$_4$ lattice model in regime 2- from the Bethe ansatz solution. This model provides a realisation of the integrable $\phi(1,2)$ perturbation of the c=7/10 conformal field theory, which is known to describe the off-critical thermal behaviour of the tricritical Ising model. The E$_7$ masses predicted from purely elastic scattering theory follow in the approach to criticality. Universal amplitudes for the tricritical Ising model are calculated.