Yang-Lee Edge Singularity by Real Space Renormalization Group (original) (raw)

Springer eBooks, 1981

Abstract

Quite a long time ago Yang and Lee [1] pointed out the importance of the relationship between the zeros of the partition function and the singularities of thermodynamic quantities occuring in a second order phase transition. They also proved the theorem that for the ferromagnetic Ising model these zeros lie on the unit circle in the complex activity plane z = exp(-2h/kT) where h is a complex symmetry breaking field and T is the temperature. In the thermodynamic limit they are distributed by some density g(h). Above TC this distribution has a gap around the real axis, which closes when approaching TC. Since g(h) is proportional to the spontaneous magnetization, the edges of this gap are branching points for the magnetization.

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