2D Ising Field Theory in a Magnetic Field: The Yang-Lee Singularity

TL;DR

This paper investigates the structure of the Yang-Lee edge singularity in Ising Field Theory under imaginary magnetic fields, using numerical methods to analyze irrelevant operators and their effects on the singular behavior.

Contribution

It provides a detailed numerical analysis of the subleading singular terms in the Yang-Lee edge singularity, focusing on irrelevant operators and their couplings in the Ising Field Theory.

Findings

Estimated couplings for the least irrelevant operators, including $T\bar T$ and a descendant operator.

Analyzed the universal properties of the $T\bar T$ deformation.

Established analytic properties of the particle mass as a function of complex magnetic field.

Abstract

We study Ising Field Theory (the scaling limit of Ising model near the Curie critical point) in pure imaginary external magnetic field. We put particular emphasis on the detailed structure of the Yang-Lee edge singularity. While the leading singular behavior is controlled by the Yang-Lee fixed point ($=$ minimal CFT ${\cal M}_{2/5}$), the fine structure of the subleading singular terms is determined by the effective action which involves a tower of irrelevant operators. We use numerical data obtained through the "Truncated Free Fermion Space Approach" to estimate the couplings associated with two least irrelevant operators. One is the operator $T{\bar T}$, and we use the universal properties of the $T{\bar T}$ deformation to fix the contributions of higher orders in the corresponding coupling parameter $\alpha$. Another irrelevant operator we deal with is the descendant $L_{-4}{\bar L}_{-4}\phi$ of the relevant primary $\phi$ in ${\cal M}_{2/5}$. The significance of this operator is that it is the lowest dimension operator which breaks integrability of the effective theory. We also establish analytic properties of the particle mass $M$ ($=$ inverse correlation length) as the function of complex magnetic field.