Correlation Functions in the Two-dimensional Ising Model in a Magnetic Field at $T=T_c$

TL;DR

This paper computes exact form factors for the energy operator in the 2D Ising model at critical temperature with a magnetic field, enabling detailed large-distance correlation analysis.

Contribution

It provides the first exact calculation of two-particle form factors for the energy operator in this setting, expanding understanding of correlation functions at criticality.

Findings

Exact two-particle form factors for the energy operator are obtained.

Large distance expansions for correlators are derived.

Results enhance the analytical understanding of the Ising model in a magnetic field.

Abstract

The one and two-particle form factors of the energy operator in the two-dimensional Ising model in a magnetic field at $T=T_c$ are exactly computed within the form factor bootstrap approach. Together with the matrix elements of the magnetisation operator already computed in ref.\,\cite{immf}, they are used to write down the large distance expansion for the correlators of the two relevant fields of the model.