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

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

2000-04-04

arxiv.org/abs/math-ph/0004003v2

Phys. Rev. Lett. 84 (2000), no. 21, 4794-4797

Physics

Mathematical Physics

4 pgs, 2 figs, to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.84.4794

We present a general, rigorous theory of Lee-Yang zeros for models with first-order phase transitions that admit convergent contour expansions. We 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 low-temperature Ising and Blume-Capel models, and the $q$-state Potts model for $q$ large enough.

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