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.

6 pages, no figures

References in corpus (1)

• General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions

Cited by in corpus (5)

• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Thin Fisher Zeroes
• Partition function zeros at first-order phase transitions: A general analysis
• Some New Exact Results for the q-State Potts Model on Ladder Graphs
• Chaotic renormalization group flow and entropy gradients over Haros graphs