Lattice Ising Model in a Field: E8 Scattering Theory

Zamolodchikov found an integrable field theory related to the Lie algebra E8, which describes the scaling limit of the Ising model in a magnetic field. He conjectured that there also exist solvable lattice models based on E8 in the universality class of the Ising model in a field. The dilute A3 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 Z2 symmetry between the states. The expected direct relation of the model with E8 has not been found hitherto. In this letter we study the thermodynamics of the dilute A3 model and show that in the scaling limit it exhibits an appropriate E8 structure, which naturally leads to the E8 scattering theory for massive excitations over the ground state.