arXiv subjects

Hao-Lan Xu

Publications and source records attributed to Hao-Lan Xu.

4 recordsLinked to original sources

arXiv2024

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

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 $ξ= h/|m|^{\frac{15}{8}}$, or related parameter $η= m / h^{\frac{8}{15}}$. 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 $ξ$ via associated low-T dispersion relation. Also, we put forward the "extended analyticity" conjecture for $M_1$ in the complex $η$-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.

hep-th↗

arXiv2023

Ising Field Theory in a magnetic field: $φ^3$ coupling at $T > T_c$

We study the "three particle coupling" $Γ_{11}^{1}(ξ)$, in $2d$ Ising Field Theory in a magnetic field, as the function of the scaling parameter $ξ:=h/(-m)^{15/8}$, where $m \sim T_c-T$ and $h \sim H$ are scaled deviation from the critical temperature and scaled external field, respectively. The "$φ^3$ coupling" $Γ_{11}^1$ is defined in terms of the residue of the $2 \to 2$ elastic scattering amplitude at its pole associated with the lightest particle itself. We limit attention to the High-Temperature domain, so that $m$ is negative. We suggest "standard analyticity": $(Γ_{11}^1)^2$, as the function of $u:=ξ^2$, is analytic in the whole complex $u$-plane except for the branch cut from $-\infty$ to $-u_0 \approx -0.03585$, the latter branching point $-u_0$ being associated with the Yang-Lee edge singularity. Under this assumption, the values of $Γ_{11}^1$ at any complex $u$ are expressed through the discontinuity across the branch cut. We suggest approximation for this discontinuity which accounts for singular expansion of $Γ_{11}^1$ near the Yang-Lee branching point, as well as its known asymptotic at $u\to +\infty$. The resulting dispersion relation agrees well with known exact data, and with numerics obtained via Truncated Free Fermion Space Approach. This work is part of extended project of studying the S-matrix of the Ising Field Theory in a magnetic field.

hep-th↗

arXiv2022

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

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 $α$. Another irrelevant operator we deal with is the descendant $L_{-4}{\bar L}_{-4}ϕ$ of the relevant primary $ϕ$ 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.

hep-th↗

arXiv2017

Tracing Primordial Black Holes in Nonsingular Bouncing Cosmology

We in this paper investigate the formation and evolution of primordial black holes (PBHs) in nonsingular bouncing cosmologies. We discuss the formation of PBH in the contracting phase and calculate the PBH abundance as a function of the sound speed and Hubble parameter. Afterwards, by taking into account the subsequent PBH evolution during the bouncing phase, we derive the density of PBHs and their Hawking radiation. Our analysis shows that nonsingular bounce models can be constrained from the backreaction of PBHs.

gr-qc↗