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arXiv · 2405.09091

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

Hao-Lan Xu
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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.

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Hao-Lan Xu. 2024-05-15. On the analyticity of the lightest particle mass of Ising field theory in a magnetic field. https://arxiv.org/abs/2405.09091

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