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

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 $f_s{\xi }^2=0.061\mathrm{728...}$ as $h\to 0$ in precise agreement with the result obtained by Delfino and Mussardo via the form-factor bootstrap approach.

7 pages, Latex

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