Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model

 

 

We consider [1] a simple generalization of the well-known Ising model allowing for vacancies i.e. spins to be absent. In two dimensions this model has a tricritical point which is described by the tricritical Ising model. The thermal deformation of the tricritical point can be described by an integrable field theory in the scaling limit. It is called the $E_7$ model and has seven stable particles with known scattering amplitudes. The model possesses a low-temperature/high-temperature duality, reminiscent of the Kramers--Wannier duality in the Ising model. However, there are two distinct order operators with the corresponding disorder ones. Using bootstrap principles and exploiting the duality, we construct the matrix elements (form factors) of the order/disorder operators between the ground state and one- and two-particle states. Utilizing Hamiltonian truncation methods and the so-called $Delta$-theorem we verify the validity of the construction. Using the form factors, we calculate one- and two-particle contributions to the dynamical structure factors of the theory, which might be accessible for experimental study.
 

 

[1]: A. Cortés Cubero, R. M. Konik, M. Lencsés, G. Mussardo, G. Takács: arXiv:2109.09767