Lattice Ising model in a field: E 8 scattering theory

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 Z 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.