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

A bstract We study solutions of the Thermodynamic Bethe Ansatz equations for relativistic theories defined by the factorizable S -matrix of an integrable QFT deformed by CDD factors. Such S -matrices appear under generalized TTbar deformations of integrable QFT by special irrelevant operators. The TBA equations, of course, determine the ground state energy E ( R ) of the finite-size system, with the spatial coordinate compactified on a circle of circumference R . We limit attention to theories involving just one kind of stable particles, and consider deformations of the trivial (free fermion or boson) S -matrix by CDD factors with two elementary poles and regular high energy asymptotics — the “2CDD model”. We find that for all values of the parameters (positions of the CDD poles) the TBA equations exhibit two real solutions at R greater than a certain parameter-dependent value R * , which we refer to as the primary and secondary branches. The primary branch is identified with the standard iterative solution, while the secondary one is unstable against iterations and needs to be accessed through an alternative numerical method known as pseudo-arc-length continuation. The two branches merge at the “turning point” R * (a square-root branching point). The singularity signals a Hagedorn behavior of the density of high energy states of the deformed theories, a feature incompatible with the Wilsonian notion of a local QFT originating from a UV fixed point, but typical for string theories. This behavior of E ( R ) is qualitatively the same as the one for standard TTbar deformations of local QFT.