Kinetic Ising models with self-interaction: Sequential and parallel updating
Kinetic Ising models with self-interaction: Sequential and parallel updating
复制标题
具有自交互作用的动力学 Ising 模型：顺序和并行更新
DOI：
10.1103/physreve.101.012122
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发表时间：
2020
影响因子：
2.4
通讯作者：
Machta, Jonathan
中科院分区：
文献类型：
--
作者：
Nareddy, Vahini Reddy;Machta, Jonathan
在随机顺序更新和并行更新的情况下，研究了正方形晶格上既有最近邻相互作用又有自相互作用的动力学伊辛模型。用蒙特卡罗模拟和解析近似研究了平衡相图和临界动力学。吉布斯分布中描述平衡性质的哈密顿量对于顺序更新和并行更新是不同的，但在这两种情况下都具有多自旋和非最近邻耦合。对于并行更新，系统是一个概率元胞自动机，并且平衡分布满足关于动力学的详细平衡[E.N.M.Cirillo，P.Y.Louis，W.M.Ruszel和C.Spitoni，混沌孤子Fractals，36(2014)CSFOEH0960-077910.1016/j.chaos.2013.12.001].在平行动力学的弱自作用极限下，奇偶亚晶格几乎解耦，在临界区和低温区出现棋盘花样，导致了临界线形状的奇异行为。对于顺序更新，平衡吉布斯分布满足全局平衡但不满足详细平衡，哈密顿量是在弱最近邻动力相互作用极限下微扰得到的。在强自作用极限下，用最近邻哈密顿量描述并行和顺序更新的平衡性质，其相互作用强度是动力学模型的两倍。
Kinetic Ising models on the square lattice with both nearest-neighbor interactions and self-interaction are studied for the cases of random sequential updating and parallel updating. The equilibrium phase diagrams and critical dynamics are studied using Monte Carlo simulations and analytic approximations. The Hamiltonians appearing in the Gibbs distribution describing the equilibrium properties differ for sequential and parallel updating but in both cases feature multispin and non-nearest-neighbor couplings. For parallel updating the system is a probabilistic cellular automaton and the equilibrium distribution satisfies detailed balance with respect to the dynamics [E. N. M. Cirillo, P. Y. Louis, W. M. Ruszel and C. Spitoni, Chaos Solitons Fractals 64, 36 (2014)CSFOEH0960-077910.1016/j.chaos.2013.12.001]. In the limit of weak self-interaction for parallel dynamics, odd and even sublattices are nearly decoupled and checkerboard patterns are present in the critical and low temperature regimes, leading to singular behavior in the shape of the critical line. For sequential updating the equilibrium Gibbs distribution satisfies global balance but not detailed balance and the Hamiltonian is obtained perturbatively in the limit of weak nearest-neighbor dynamical interactions. In the limit of strong self-interaction the equilibrium properties for both parallel and sequential updating are described by a nearest-neighbor Hamiltonian with twice the interaction strength of the dynamical model.