The inversion relation and the dilute A_{3,4,6} eigenspectrum

TL;DR

This paper extends Baxter's approach to predict eigenspectra of dilute A models for L=4 and L=6, revealing simple relations in mass calculations linked to E_7 and E_6 spectra.

Contribution

It introduces the dilute A_L inversion relation to predict eigenspectra for L=4 and L=6, expanding understanding beyond the previously studied L=3 case.

Findings

Inversion relation predicts eigenspectra for L=4 and L=6.

Simple relation for next-to-leading mass terms.

Consistent with E_7 and E_6 mass spectra.

Abstract

On the basis of the result obtained by applying Baxter's exact perturbative approach to the dilute A_3 model to give the E_8 mass spectrum, the dilute A_L inversion relation was used to predict the eigenspectra in the L=4 and L=6 cases (corresponding to E_7 and E_6 respectively). In calculating the next-to-leading term in the correlation lengths, or equivalently masses, the inversion relation condition gives a surprisingly simple result in all three cases, and for all masses.