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

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.

© American Physical Society (APS) [Mutual information and breakdown of the Perron-Frobenius scenario in zero-temperature triangular Ising antiferromagnets on cylinders. Physical Review E 105, 4 (2022)]

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Work Title Mutual information and breakdown of the Perron-Frobenius scenario in zero-temperature triangular Ising antiferromagnets on cylinders
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Open Access
Creators
  1. Amir Nourhani
  2. Vincent H. Crespi
  3. Paul E. Lammert
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Physical Review E
Publication Date April 5, 2022
Publisher Identifier (DOI)
  1. https://doi.org/10.1103/PhysRevE.105.044105
Deposited May 19, 2023

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  • Created
  • Added PRE-final.pdf
  • Added Creator Amir Nourhani
  • Added Creator Vincent H. Crespi
  • Added Creator Paul E. Lammert
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