1D Potts, Yang-Lee Edges and Chaos
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0010372,
title = {1D Potts, Yang-Lee Edges and Chaos},
author = {B. P. Dolan and D. Johnston},
journal= {arXiv preprint arXiv:cond-mat/0010372},
year = {2015}
}
Comments
6 pages, no figures