Mutual information and breakdown of the Perron-Frobenius scenario in zero-temperature triangular Ising antiferromagnets on cylinders

Amir Nourhani; Vincent H Crespi; Paul E Lammert

doi:10.1103/PhysRevE.105.044105

Mutual information and breakdown of the Perron-Frobenius scenario in zero-temperature triangular Ising antiferromagnets on cylinders

Phys Rev E. 2022 Apr;105(4-1):044105. doi: 10.1103/PhysRevE.105.044105.

Authors

Amir Nourhani^{1

2

3}, Vincent H Crespi^{4

5

6}, Paul E Lammert⁴

Affiliations

¹ Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA.
² Biomimicry Research and Innovation Center, University of Akron, Akron, Ohio 44325, USA.
³ Departments of Biology, Mathematics, and Chemical, Biomolecular and Corrosion Engineering, University of Akron, Akron, Ohio 44325, USA.
⁴ Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
⁵ Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
⁶ Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA.

PMID: 35590530
DOI: 10.1103/PhysRevE.105.044105

Abstract

A nominally two-dimensional spin model wrapped onto a cylinder can profitably be viewed, especially for long cylinders, as a one-dimensional chain. Each site of such a chain is a ring of spins with a complex state space. Traditional correlation functions are inadequate for the study of correlations in such a system and need to be replaced with something like mutual information. Being induced purely by frustration, the disorder of a cylindrical zero-temperature triangular Ising antiferromagnet (TIAFM) and attendant correlations have a chance of evading the consequences of the Perron-Frobenius theorem which describes and constrains correlations in thermally disordered one-dimensional systems. Correlations in such TIAFM systems and the aforementioned evasion are studied here through a fermionic representation. For cylindrical TIAFM models with open boundary conditions, we explain and derive the following characteristics of end-to-end mutual information: period-three oscillation of the decay length, halving of the decay length compared to what Perron-Frobenius predicts on the basis of transfer matrix eigenvalues, and subexponential decay-inverse square in the length-for certain systems.