Ground-state energy and frustration of the Sherrington-Kirkpatrick model and related models
Ground-state energy and frustration of the Sherrington-Kirkpatrick model and related models
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谢林顿-柯克帕特里克模型及相关模型的基态能量和挫败感
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
S. Kobe
中科院分区：
文献类型：
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作者：
S. Kobe
精确的基态计算的Sherrington-Kirkpatrick（SK）自旋玻璃含有高达N=90自旋。从失配参数的N依赖性中发现了基态每自旋能量e^{\infty}_0 =-0.7637\pm 0.0004$，这是对系统挫折的度量.结果与两个相关的模型，这可以通过取代所有的相互作用的SK模型相同强度的铁磁或反铁磁的。引入了一个参数x，它描述了这些类型的模型中反铁磁相互作用的分数。从有限模型的x依赖性可以得出结论，SK模型$（x=0.5）$指定铁磁状态$（x 0.5）$之间的转变。
Exact ground states are calculated for the Sherrington-Kirkpatrick (SK) spin-glass containing up to N=90 spins. A ground-state energy per spin $e^{\infty}_0 = - 0.7637 \pm 0.0004$ is found from the $N$ dependence of the misfit parameter, which is a measure of frustration of the system. The results are compared with those of two related models, which can be introduced by replacing all interactions of the SK model by ferromagnetic or antiferromagnetic ones of the same strengths. A parameter $x$ is introduced, which describes the fraction of antiferromagnetic interactions in these types of models. From the $x$ dependence of finite models it is concluded, that the the SK model $(x=0.5)$ assigns a transition between a ferromagnetic state $(x 0.5)$.