1D Potts, Yang-Lee Edges and Chaos

Details 1D Potts, Yang-Lee Edges and Chaos 1D Potts, Yang-Lee Edges and Chaos

2000-10-24

arxiv.org/abs/cond-mat/0010372v1

Phys.Rev.E65.057103,2002

Physics

Condensed Matter

Statistical Mechanics

6 pages, no figures

Scientific paper

It is known that the (exact) renormalization transformations for the one-dimensional Ising model in field can be cast in the form of a logistic map f(x) = 4 x (1 - x) with x a function of the Ising couplings. Remarkably, the line bounding the region of chaotic behaviour in x is precisely that defining the Yang-Lee edge singularity in the Ising model. In this paper we show that the one dimensional q-state Potts model for q greater than or equal to 1 also displays such behaviour. A suitable combination of Potts couplings can again be used to define an x satisfying f(x) = 4 x (1 -x). The Yang-Lee zeroes no longer lie on the unit circle in the complex z = exp (h) plane, but their locus is still reproduced by the boundary of the chaotic region in the logistic map.

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