Hereditary structure in Hamiltonians: Information geometry of Ising spin chains
Hereditary structure in Hamiltonians: Information geometry of Ising spin chains
复制标题
DOI：
10.1016/j.physleta.2009.12.022
复制
发表时间：
2010-02-01
影响因子：
2.6
通讯作者：
Shuto, Shigeru
中科院分区：
文献类型：
--
作者：
Fujiwara, Akio;Shuto, Shigeru
这封信处理的问题近似的规范状态的伊辛自旋链的一个层次系列的独立和相同分布的集群状态。基于信息几何，它表明，每个集团态的有效哈密顿量的结构是从总的哈密顿量继承。这一事实部分地证明了平均场理论的方法论。从统计假设检验的角度进一步分析了相变问题。(C)2009 Elsevier B.V.保留所有权利。
This Letter deals with the problem of approximating the canonical state of an Ising spin chain by a hierarchical series of independent and identically distributed cluster states. Based on information geometry, it is shown that the structure of the effective Hamiltonian for each cluster state is inherited from the total Hamiltonian. This fact partly justifies the methodology of mean field theories. The issue of a phase transition is further analyzed from the point of view of statistical hypothesis testing. (C) 2009 Elsevier B.V. All rights reserved.