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

Abstract

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 M $$ \mathcal{M} $$ 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 ¯ $$ T\overline{T} $$ , and we use the universal properties of the T T ¯ $$ T\overline{T} $$ 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 ¯ $$ \overline{L} $$ _ 4 ϕ of the relevant primary ϕ in M $$ \mathcal{M} $$ 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.

Keywords

• Field Theories in Lower Dimensions
• Integrable Field Theories
• Renormalization Group
• Scale and Conformal Symmetries