We study the numerical simulation of the shaken dynamics, a parallel Markovian dynamics for spin systems with local interaction and transition probabilities depending on the two parameters q and J that “tune” the geometry of the underlying lattice. The analysis of the mixing time of the Markov chain and the evaluation of the spin-spin correlations as functions of q and J, make it possible to determine in the (q, J) plane a phase transition curve separating the disordered phase from the ordered one. The relation between the equilibrium measure of the shaken dynamics and the Gibbs measure for the Ising model is also investigated. Finally two different coding approaches are considered for the implementation of the dynamics: a multicore CPU approach, coded in Julia, and a GPU approach coded with CUDA.

我们研究了振动动力学的数值模拟，这是一种用于自旋系统的并行马尔可夫动力学，其局部相互作用和跃迁概率取决于“调整”底层晶格几何形状的两个参数q和J。马尔可夫链混合时间的分析和作为q和J函数的自旋-自旋相关性的评估，使得在 ( q ,  J) 平面相变曲线将无序相与有序相分开。还研究了振动动力学的平衡测度与 Ising 模型的 Gibbs 测度之间的关系。最后，考虑了两种不同的编码方法来实现动态：一种用 Julia 编码的多核 CPU 方法，以及一种用 CUDA 编码的 GPU 方法。