General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions

We present a general, rigorous theory of Lee-Yang zeros for models with first-order phase transitions and derive formulas for the positions and the density of the zeros. In particular, we show that for models without symmetry, the curves on which the zeros lie are generically not circles, and can have topologically nontrivial features, such as bifurcation. Our results are illustrated in three models in a complex field: the Ising magnet, the Blume-Capel model, and the Potts model.