Department of Computational Biology, AlbaNova University Center, SE-106 91 Stockholm, Sweden.
Departments of Applied Physics and Computer Science, Aalto University, FIN-00076 Aalto, Finland.
Phys Rev E. 2017 May;95(5-1):052119. doi: 10.1103/PhysRevE.95.052119. Epub 2017 May 12.
We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.
我们提出了一种封闭表示相互作用的伊辛自旋的连续时间动力学的主方程的替代方法。该方法利用随机点过程理论推导出局部条件概率的主方程。我们通过研究两个已知的情况，即平均场铁磁体的动力学和一维伊辛系统的动力学，对我们的解进行了分析测试。我们提出了数值结果，将我们的预测与在具有有限连接性的随机图上的三个不同模型中的蒙特卡罗模拟进行了比较：伊辛铁磁体、随机场伊辛模型和维亚纳-布雷玻色自旋玻璃模型。
