Directed percolation, fractal roots and the Lee–Yang theorem

In the directed percolation model we consider the probability p of having an open bond as a complex parameter. We show that the roots of the survival probability P N ( p) for a square lattice of N rows distribute themselves in a fractal manner in the complex p-plane. These roots have an accumulation...

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Bibliographic Details
Published in:Physica A 2001-06, Vol.295 (1), p.128-131
Main Authors: Arndt, P.F, Dahmen, S.R, Hinrichsen, H
Format: Article
Language:English
Subjects:
Complex Analysis
Percolation model
Phase transitions
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Summary:In the directed percolation model we consider the probability p of having an open bond as a complex parameter. We show that the roots of the survival probability P N ( p) for a square lattice of N rows distribute themselves in a fractal manner in the complex p-plane. These roots have an accumulation point on the real axis which coincides with the critical probability p c =0.6447.
ISSN:0378-4371
1873-2119
DOI:10.1016/S0378-4371(01)00064-4