Role of the interaction matrix in mean-field spin glass models.
Role of the interaction matrix in mean-field spin glass models.
复制标题
相互作用矩阵在平均场自旋玻璃模型中的作用。
DOI：
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复制
发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Lefevre
中科院分区：
文献类型：
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作者：
R. Cherrier;D. Dean;A. Lefevre
研究了双自旋伊辛自旋玻璃的平均场模型，其相互作用矩阵取自系综且在O(N)变换下是不变的。一般的研究表明，自旋玻璃相变的性质可以从相互作用矩阵的本征值谱中推断出来。导出了一种简单的复制方法来实现O(N)无序的平均化。通过对大系统的蒙特卡罗模拟和对小系统的精确计数，验证了分析结果。
Mean-field models of two-spin Ising spin glasses with interaction matrices taken from ensembles that are invariant under O(N) transformations are studied. A general study shows that the nature of the spin glass transition can be deduced from the eigenvalue spectrum of the interaction matrix. A simple replica approach is derived to carry out the average over the O(N) disorder. The analytic results are confirmed by the extensive Monte Carlo simulations for large system sizes and by the exact enumeration for small system sizes.