Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model

TL;DR

This paper derives the exact correlation length for certain lattice models, including the E_8 Ising model, confirming universal amplitude predictions and aligning with previous bootstrap results.

Contribution

It provides an exact derivation of the correlation length for the E_8 lattice Ising model using a perturbation approach, confirming universality of the amplitude.

Findings

Exact correlation length for A_3 model in regimes 1 and 2

Universal amplitude of the free energy and correlation length product

Agreement with form-factor bootstrap results

Abstract

The perturbation approach is used to derive the exact correlation length $\xi$ of the dilute A_L lattice models in regimes 1 and 2 for L odd. In regime 2 the A_3 model is the E_8 lattice realisation of the two-dimensional Ising model in a magnetic field h at T=T_c. When combined with the singular part f_s of the free energy the result for the A_3 model gives the universal amplitude $f_s \xi^2 = 0.061~728...$ as $h\to 0$ in precise agreement with the result obtained by Delfino and Mussardo via the form-factor bootstrap approach.