Correlation lengths and E_8 mass spectrum of the dilute A_3 lattice model

TL;DR

This paper derives correlation lengths and mass spectra for the dilute A_3 lattice model using Bethe Ansatz, confirming the E_8 spectrum predicted by Zamolodchikov in the critical limit.

Contribution

It provides a direct lattice calculation of the E_8 mass spectrum for the dilute A_3 model, connecting lattice results with conformal field theory predictions.

Findings

Correlation lengths and mass gaps derived from Bethe Ansatz.

Mass spectrum reduces to E_8 masses at criticality.

Consistent string types identified in the high field limit.

Abstract

The exact perturbation approach is used to derive the elementary correlation lengths $\xi_i$ and related mass gaps $m_i$ of the two-dimensional dilute A_L lattice model in regimes 1 and 2 for L odd from the Bethe Ansatz solution. In regime 2 the A_3 model is the E_8 lattice realisation of the two-dimensional Ising model in a magnetic field at T=T_c. The calculations for the A_3 model in regime 2 start from the eight thermodynamically significant string types found in previous numerical studies. These string types are seen to be consistent in the ordered high field limit. The eight masses obtained reduce with the approach to criticality to the E_8 masses predicted by Zamolodchikov, thus providing a further direct lattice determination of the E_8 mass spectrum.