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Lattice Ising model in a field: E$_8$ scattering theory

V. V. Bazhanov·B. Nienhuis·S. O. Warnaar
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Abstract

Zamolodchikov found an integrable field theory related to the Lie algebra E$_8$, which describes the scaling limit of the Ising model in a magnetic field. He conjectured that there also exist solvable lattice models based on E$_8$ in the universality class of the Ising model in a field. The dilute A$_3$ model is a solvable lattice model with a critical point in the Ising universality class. The parameter by which the model can be taken away from the critical point acts like a magnetic field by breaking the $\Integer_2$ symmetry between the states. The expected direct relation of the model with E$_8$ has not been found hitherto. In this letter we study the thermodynamics of the dilute A$_3$ model and show that in the scaling limit it exhibits an appropriate E$_8$ structure, which naturally leads to the E$_8$ scattering theory for massive excitations over the ground state.

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V. V. Bazhanov, B. Nienhuis, S. O. Warnaar. 1993-12-21. Lattice Ising model in a field: E$_8$ scattering theory. https://doi.org/10.1016/0370-2693(94)91107-x

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