Roaming form factors for the tricritical to critical Ising flow

TL;DR

This paper investigates the massless renormalization group flow from the tricritical to the critical Ising model using form factors derived from the sinh-Gordon S-matrix, revealing new connections between form factors and operators.

Contribution

It introduces a method to obtain form factors for the massless flow by analytic continuation, linking sinh-Gordon form factors to order and disorder operators in the Ising model.

Findings

Roaming limits of sinh-Gordon form factors match those of Ising order/disorder operators.

Constructed form factors for a semi-local field related to the twist field.

Established a connection between sinh-Gordon form factors and massless flow operators.

Abstract

We study the massless flows described by the staircase model introduced by Al.B. Zamolodchikov through the analytic continuation of the sinh-Gordon S-matrix, focusing on the renormalisation group flow from the tricritical to the critical Ising model. We show that the properly defined roaming limits of certain sinh-Gordon form factors are identical to the form factors of the order and disorder operators for the massless flow. As a by-product, we also construct form factors for a semi-local field in the sinh-Gordon model, which can be associated with the twist field in the ultraviolet limiting free massless bosonic theory.