On the eigenvalue spectrum of the susceptibility matrix for random spin systems
On the eigenvalue spectrum of the susceptibility matrix for random spin systems
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DOI：
10.1088/0022-3719/15/23/008
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发表时间：
1982-08
期刊：
影响因子：
--
通讯作者：
A. Bray;M. .. Moore
中科院分区：
文献类型：
--
作者：
A. Bray;M. .. Moore
讨论了随机自旋系统磁化率矩阵逆的本征值和本征向量。在由最小本征值消失引起的相变处，证明了相应的本征矢必须被扩展，并且态密度必须在零本征值处为零。在转变温度以上，广义Griffiths奇点与具有任意小本征值的局域态的存在有关。对于无限大的自旋维度，本征值问题等价于具有相关的对角和非对角无序的Anderson问题。
The eigenvalues and eigenvectors of the inverse of the susceptibility matrix are discussed for random spin systems. At a phase transition precipitated by the vanishing of the smallest eigenvalue it is shown that the corresponding eigenvector must be extended, and that the density of states must vanish at zero eigenvalue. Above the transition temperature, generalised Griffiths singularities are associated with the existence of localised states with arbitrarily small eigenvalues. For infinite spin dimensionality the eigenvalue problem is equivalent to an Anderson problem with correlated diagonal and off-diagonal disorder.