Thermodynamc Approach to Three-Site Antiferromagnetic Ising Model in Chaotic Region

TL;DR

This paper explores the chaotic behavior of a three-site antiferromagnetic Ising model on a Husimi tree, revealing multifractal attractors and phase transitions through thermodynamic formalism.

Contribution

It introduces a thermodynamic approach to analyze chaos in the Ising model, showing nonanalyticities and parameter-dependent phase transitions.

Findings

Multifractal scaling in strange attractors

Nonanalytic free energy and entropy

Phase transition temperature varies with parameters

Abstract

The chaotic properties of the three-site antiferromagnetic Ising model on Husimi tree are investigated in magnetic field. Macroscopic quantity of three-site antiferromagnetic Ising model is generated by one dimensional map. It is shown that in certain parameter setting strange attractors of this map exhibit multifractal scaling. By applying thermodynamic formalism we find nonanalyticity in free energy as well as in entropy. We show that the temperature of phase transition depends on parameter of model and varies from negative to positive value.