arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0710.5403cond-mat.stat-mechcond-mat.dis-nn
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自旋玻璃的能量景观网络

The energy landscape networks of spin-glasses

Hamid Seyed-allaei, Hamed Seyed-allaei, Mohammad Reza Ejtehadi

摘要:

我们研究了自旋玻璃模型的能量景观的拓扑结构,并通过观察固有结构的连通性和不连通性图来研究挫折对它的影响。连通性网络显示了能量最小值的邻近性,而不连通性网络告诉我们能量势垒的高度。这两个图是由一个二维正方形格子的挫折自旋玻璃与最近邻相互作用的大小为27自旋的精确计数。能量景观极小值的枚举以及分析平均场近似表明,这些极小值具有高斯分布,并且连通图具有形状$κ=8.22$和尺度$λ=4.84$的对数威布尔度分布。为了研究阻挫效应对这些结果的影响,我们引入了一个非阻挫自旋玻璃模型,并证明了其连通图的度分布呈现幂律行为,指数为-3.46,这与蛋白质和Lennard-Jones团簇的幂律行为相似.

英文摘要:

We have studied the topology of the energy landscape of a spin-glass model and the effect of frustration on it by looking at the connectivity and disconnectivity graphs of the inherent structure. The connectivity network shows the adjacency of energy minima whereas the disconnectivity network tells us about the heights of the energy barriers. Both graphs are constructed by the exact enumeration of a two-dimensional square lattice of a frustrated spin glass with nearest-neighbor interactions up to the size of 27 spins. The enumeration of the energy-landscape minima as well as the analytical mean-field approximation show that these minima have a Gaussian distribution, and the connectivity graph has a log-Weibull degree distribution of shape $κ=8.22$ and scale $λ=4.84$. To study the effect of frustration on these results, we introduce an unfrustrated spin-glass model and demonstrate that the degree distribution of its connectivity graph shows a power-law behavior with the -3.46 exponent, which is similar to the behavior of proteins and Lennard-Jones clusters in its power-law form.

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