Biskup M, Borgs C, Chayes JT, Kleinwaks LJ, Kotecky R
Microsoft Research, One Microsoft Way, Redmond, Washington 98052, USA.
Phys Rev Lett. 2000 May 22;84(21):4794-7. doi: 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 large q.
我们为具有一阶相变且允许收敛轮廓展开的模型提出了一种通用、严谨的Lee-Yang零点理论。我们推导了零点位置和密度的公式。特别地，我们表明，对于没有对称性的模型，零点所在的曲线通常不是圆，并且可以具有拓扑非平凡的特征，如分岔。我们的结果在复场中的三个模型中得到了说明：低温伊辛模型和布鲁姆-卡佩尔模型，以及大q值的q态Potts模型。
