On the analyticity of the lightest particle mass of Ising field theory in a magnetic field

Abstract

We study the scaling functions associated with the lightest particle mass $M_1$ in 2d Ising field theory in external magnetic field. The scaling functions depend on the scaling parameter $\xi =h/|m{|}^{\frac{15}{8}}$, or related parameter $\eta =m/h^{\frac{8}{15}}$. Analytic properties of $M_1$ in the high-T domain were discussed in arXiv:2203.11262. In this work, we study analyticity of $M_1$ in the low-T domain. Important feature of this analytic structure is represented by the Fisher-Langer's branch cut. The discontinuity across this branch cut determines the behavior of $M_1$ at all complex $\xi$ via associated low-T dispersion relation. Also, we put forward the "extended analyticity" conjecture for $M_1$ in the complex $\eta$-plane, similar to the analyticity of the free energy density previously proposed in arXiv:hep-th/0112167. The extended analyticity implies the "extended dispersion relation", which we verify against the numerics from the Truncated Free Fermion Approach (TFFSA), giving strong support to the conjecture.

arXiv comment38 pages, 13 figures