Mutual information and breakdown of the Perron-Frobenius scenario in zero-temperature triangular Ising antiferromagnets on cylinders
Mutual information and breakdown of the Perron-Frobenius scenario in zero-temperature triangular Ising antiferromagnets on cylinders
复制标题
圆柱体上零温三角伊辛反铁磁体 Perron-Frobenius 场景的互信息和分解
DOI：
10.1103/physreve.105.044105
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发表时间：
2022
影响因子：
2.4
通讯作者：
Lammert, Paul E.
中科院分区：
文献类型：
--
作者：
Nourhani, Amir;Crespi, Vincent H.;Lammert, Paul E.
包装在圆柱体上的名义上的二维自旋模型可以有利可图地视为一维链，特别是对于长圆柱体。这样一个链的每个位置都是一个具有复杂状态空间的自旋环。传统的相关函数不足以研究这样一个系统中的相关性，需要用像互信息这样的东西来取代。柱形零温三角伊辛反铁磁体(TIAFM)的无序和伴随的关联纯粹是由受挫引起的，它有机会避开描述和约束一维热无序系统关联的Perron-Frobenius定理的结果。本文通过费米子表示研究了这种TIAFM系统中的关联和上述回避。对于具有开放边界条件的圆柱形TIAFM模型，我们解释和推导了端到端互信息的以下特征：对于某些系统，衰减长度的周期为3振荡，衰减长度比Perron-Frobenius根据转移矩阵本征值预测的衰减长度减半，以及亚指数衰减-长度的平方反比。
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.