Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

TL;DR

This paper develops a modified free-field representation for form factors in the Bullough-Dodd model, enabling explicit calculations and validation against bootstrap results, with applications to the Ising model in a magnetic field.

Contribution

It introduces a new free-field representation excluding two-particle minimal form factors, facilitating multi-particle form factor calculations in related models.

Findings

Derived recurrence relations for multi-particle form factors.

Validated the representation against bootstrap equation solutions.

Applied the method to the Ising model in a magnetic field.

Abstract

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed minimal models. As a significant example we consider the Ising model in a magnetic field. We check that the results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.