Yang–Lee zeros of the Yang–Lee model

To understand the distribution of the Yang–Lee zeros in quantum integrable field theories we analyse the simplest of these systems given by the 2D Yang– Lee model. The grand-canonical partition function of this quantum field theory, as a function of the fugacity z and the inverse temperature β, can be computed in terms of the thermodynamics Bethe Ansatz based on its exact S-matrix. We extract the Yang–Lee zeros in the complex plane by using a sequence of polynomials of increasing order N in z which converges to the grand-canonical partition function. We show that these zeros are distributed along curves which are approximate circles as it is also the case of the zeros for purely free theories. There is though an important difference between the interactive theory and the free theories, for the radius of the zeros in the interactive theory goes continuously to zero in the high-temperature limit β → 0 while in the free theories it remains close to 1 even for small values of β, jumping to 0 only at β = 0.