Kinetic Ising models with self-interaction: Sequential and parallel updating.,Physical Review E

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Kinetic Ising models with self-interaction: Sequential and parallel updating.
Physical Review E ( IF 2.2 ) Pub Date : 2020-01-01 , DOI: 10.1103/physreve.101.012122
Vahini Reddy Nareddy ₁ , Jonathan Machta _{1,

2}

Affiliation

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.

中文翻译：

具有自交互作用的动力学Ising模型：顺序和并行更新。

针对随机顺序更新和并行更新的情况，研究了具有最近邻相互作用和自相互作用的方格子上的动力学伊辛模型。使用蒙特卡洛模拟和解析近似法研究了平衡相图和临界动力学。出现在吉布斯分布中的哈密顿量描述了平衡特性在顺序更新和并行更新中有所不同，但在两种情况下均具有多旋转和非近邻耦合。对于并行更新，系统是一个概率性的细胞自动机，并且平衡分布满足动力学方面的详细平衡[ENM Cirillo，PY Louis，WM Ruszel和C. Spitoni，Chaos Solitons Fractals 64，36（2014）CSFOEH0960-077910.1016 / j .chaos.2013.12.001]。在平行动力学的弱自相互作用限制下，奇数和偶数子晶格几乎解耦，并且在临界和低温状态下都存在棋盘图案，从而导致临界线形状出现奇异行为。为了顺序更新平衡，吉布斯分布满足整体平衡，但不满足详细平衡，并且在弱的最近邻动力学相互作用的极限中微扰地获得了哈密顿量。在强烈的自交互作用的限制下，并行更新和顺序更新的平衡特性由最接近的哈密顿量描述，其动力学强度是动力学模型的两倍。导致临界线形状出现异常行为。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，并且在弱的最近邻动力学相互作用的极限中微扰地获得了哈密顿量。在强烈的自交互作用的限制下，并行更新和顺序更新的平衡特性由最接近的哈密顿量描述，其动力学强度是动力学模型的两倍。导致临界线形状出现异常行为。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，并且在弱的最近邻动力学相互作用的极限中微扰地获得了哈密顿量。在强烈的自交互作用的限制下，并行更新和顺序更新的平衡特性由最接近的哈密顿量描述，其动力学强度是动力学模型的两倍。

更新日期：2020-01-15

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