Parallel dynamics of disordered Ising spin systems on finitely connected random graphs
Parallel dynamics of disordered Ising spin systems on finitely connected random graphs
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DOI：
10.1088/0305-4470/37/24/001
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发表时间：
2004-06-18
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影响因子：
--
通讯作者：
Coolen, ACC
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文献类型：
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作者：
Hatchett, JPL;Wemmenhove, B;Coolen, ACC
利用生成泛函分析方法研究了有限连通随机图上键无序伊辛自旋系统的动力学行为。这里的动态序参量不是无序平均的相关函数和响应函数（对于全连通系统），而是一种度量，它代表了给定外部扰动场路径的无序平均单自旋路径概率。在完全非对称图的极限下，我们的宏观定律已经在零外场下的单自旋路径概率方面闭合了。对于任意图形对称的一般情况下，我们计算的动力学的前几个时间步长准确，我们制定出（数值和分析）的程序来构建我们的方程的近似稳态解。模拟结果支持我们的理论预测。
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems), the dynamic order parameter is here a measure which represents the disorder-averaged single-spin path probabilities, given external perturbation field paths. In the limit of completely asymmetric graphs, our macroscopic laws close already in terms of the single-spin path probabilities at zero external field. For the general case of arbitrary graph symmetry, we calculate the first few time steps of the dynamics exactly, and we work out (numerical and analytical) procedures for constructing approximate stationary solutions of our equations. Simulation results support our theoretical predictions.