2D Ising Field Theory in a magnetic field: the Yang-Lee singularity

A bstract 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 f...

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Bibliographic Details
Published in:The journal of high energy physics 2022-08, Vol.2022 (8), p.57-41, Article 57
Main Authors: Xu, Hao-Lan, Zamolodchikov, Alexander
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Couplings
Critical point
Curie temperature
Elementary Particles
Fermions
Field Theories in Lower Dimensions
Field theory
Fine structure
Fixed points (mathematics)
High energy physics
Integrable Field Theories
Ising model
Magnetic fields
Operators (mathematics)
Particle mass
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Renormalization Group
Scale and Conformal Symmetries
Singularities
String Theory
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Summary:A bstract 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 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 T ¯ , and we use the universal properties of the T 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 L ¯ _ 4 ϕ of the relevant primary ϕ in 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP08(2022)057