Form factor bootstrap in the thermally perturbed tricritical Ising model

TL;DR

This paper develops a systematic method to compute form factors in the thermal perturbation of the tricritical Ising model, enabling detailed analysis of correlation functions near criticality.

Contribution

It introduces a new recursive structure for form factors in the $E_7$ integrable scattering framework, providing a complete mathematical proof for key fields.

Findings

Derived explicit form factors for perturbing and order/disorder fields.

Established a recursive structure encoding bound state fusion.

Enabled systematic computation of correlation functions.

Abstract

We derive a systematic construction for form factors of relevant fields in the thermal perturbation of the tricritical Ising model, an integrable model with scattering amplitudes described by the $E_7$ bootstrap. We find a new type of recursive structure encoding the information in the bound state fusion structure, which fully determines the form factors of the perturbing field and the order/disorder fields, for which we present a mathematical proof. Knowledge of these form factors enables the systematic computation of correlation functions and dynamical structure factors in systems whose dynamics is governed by the vicinity of a fixed point in the tricritical Ising universality class.