Chaotic Repellers in Antiferromagnetic Ising Model

TL;DR

This paper explores the chaotic behavior of the antiferromagnetic Ising model, establishing a connection to chaotic repellers, analyzing fractal invariants, and identifying a phase transition at a positive temperature.

Contribution

It presents the first analysis of chaos in the antiferromagnetic Ising model and links it to chaotic repellers with exact invariant measures.

Findings

Chaotic properties characterized by fractal invariants.

Identification of a phase transition at temperature β_c=0.89.

Exact connection established between the model and chaotic repellers.

Abstract

For the first time we present the consideration of the antiferromagnetic Ising model in case of fully developed chaos and obtain the exact connection between this model and chaotic repellers. We describe the chaotic properties of this statistical mechanical system via the invariants characterizing a fractal set and show that in chaotic region it displays phase transition at {\it positive} "temperature" $ \beta_c = 0.89 $. We obtain the density of the invariant measure on the chaotic repeller.