Glauber Dynamics in a Zero Magnetic Field and Eigenvalue Spacing Statistics
Glauber Dynamics in a Zero Magnetic Field and Eigenvalue Spacing Statistics
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零磁场中的格劳伯动力学和特征值间距统计
DOI：
10.1051/jp1:1996225
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
R. Mélin
中科院分区：
文献类型：
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作者：
R. Mélin
我们讨论了统计力学的各种模型（一维伊辛模型，二维伊辛模型，一维模型与无序基态，和SK模型与铁磁偏置）的Glauber矩阵的本征值间距统计。一维Ising模型的动力学是可积的，特征值间距统计是非普适的。在其他情况下，在高温状态下的特征值统计介于泊松和G.O.E之间（P（0）的数量级为0.5）。在中间温度区，统计数据是G.O.E.。在低温状态下，统计在s = 0处具有峰值。在低温区，对于无序系统，本征值凝聚在整数周围，这是因为任何自旋上的局部场永远不会消失。这个性质对于Cayley树上的Ising模型仍然有效，即使它不是无序的。我们还研究了作为温度的函数的两个最大的本征值之间的间距。这个量似乎对对称性破缺相的存在很敏感。
We discuss the eigenvalue spacing statistics of the Glauber matrix for various models of statistical mechanics (a one dimensional Ising model, a two dimensional Ising model, a one dimensional model with a disordered ground state, and a SK model with and without a ferromagnetic bias). The dynamics of the one dimensional Ising model are integrable and the eigenvalue spacing statistics are non-universal. In the other cases, the eigenvalue statistics in the high temperature regime are intermediate between Poisson and G.O.E (with P(0) of the order of 0.5). In the intermediate temperature regime, the statistics are G.O.E.. In the low temperature regime, the statistics have a peak at s = 0. In the low temperature regime, and for disordered systems, the eigenvalues condense around integers, due to the fact that the local field on any spin never vanishes. This property is still valid for the Ising model on the Cayley tree, even if it is not disordered. We also study the spacing between the two largest eigenvalues as a function of temperature. This quantity seems to be sensitive to the existence of a broken symmetry phase.