Hatchett J P L, Pérez Castillo I, Coolen A C C, Skantzos N S
Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan.
Phys Rev Lett. 2005 Sep 9;95(11):117204. doi: 10.1103/PhysRevLett.95.117204. Epub 2005 Sep 8.
We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do so, we generalize existing versions of dynamical replica theory and cavity field techniques to systems with strongly disordered and locally treelike interactions. We illustrate our results via application to, e.g., +/-J spin glasses on random graphs and of the overlap in finite connectivity Sourlas codes. All results are tested against Monte Carlo simulations.
我们研究了有限连通性的随机图上具有随机键和/或异质度分布的伊辛自旋模型中宏观可观测量的动力学，例如磁化强度和每自由度能量。为此，我们将现有的动力学复制理论和腔场技术推广到具有强无序和局部树状相互作用的系统。我们通过将结果应用于例如随机图上的±J自旋玻璃以及有限连通性索拉斯码中的重叠来进行说明。所有结果都与蒙特卡罗模拟进行了对比检验。
