In a classical work, Lee and Yang proved that zeros of certain polynomials (partition functions of Ising models) always lie on the unit circle. Distribution of these zeros control phase transitions in the model. We study this distribution for a special ?Migdal-Kadanoff hierarchical lattice?. In this case, it can be described in terms of the dynamics of an explicit rational function in two variables called the "Migdal-Kadanoff renormalization map". We prove several theorems about the dynamical properties of this map and use them to provide a rather precise description of the limiting distribution of Lee-Yang zeros for the Diamond Hierarchical Lattice. This is a joint work with Pavel Bleher and Mikhail Lyubich.