  To understand the distribution of the Yang-Lee zeros in quantum integrable
field theories we analyse the simplest of these systems given by the
two-dimensional Yang-Lee model. The grand-canonical partition function of this
quantum field theory, as a function of the fugacity z and the inverse
temperature beta, 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 beta ->0 while in the free theories it remains close to
1 even for small values of beta, jumping to 0 only at beta = 0.
