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 fir st-order phase transitions that admit convergent contour expansions. We der ive 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 l ie are generically not circles, and can have topologically nontrivial featu res, such as bifurcation. Our results are illustrated in three models in a complex field: the low-temperature Ising and Blume-Capel models, and the cl -state Potts model for large q.