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Research Report MRR97-016

Magnetic correlation length and universal amplitude of the lattice E8 Ising model

M.T. Batchelor and K.A. Seaton

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

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