Nonlinear XY and p-clock models on sparse random graphs: Mode-locking transition of localized waves
Nonlinear XY and p-clock models on sparse random graphs: Mode-locking transition of localized waves
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DOI：
10.1103/physrevb.91.054201
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发表时间：
2015-02-17
影响因子：
3.7
通讯作者：
Leuzzi, Luca
中科院分区：
文献类型：
--
作者：
Marruzzo, Alessia;Leuzzi, Luca
在二分稀疏随机图上提出了具有非线性相互作用的 XY 模型的统计力学研究。将模型属性与 p 时钟模型的属性进行比较，其中平面连续自旋被离散化为 p 值。我们测试了数值计算和模拟中使用的 XY 自旋离散近似的优点及其在给定的、与 p 相关的温度范围内的收敛极限。该模型用于描述激光器中光模式相位在临界激光阈值下的锁模转变。为每个变量节点分配一个频率，功能节点实现频率匹配条件。重要的非磁化锁相发生在相变处，其中相位的频率依赖性在很宽的频率范围内呈线性，就像在光功率阈值下的标准锁模多模激光器中一样。
A statistical mechanic study of the XY model with nonlinear interaction is presented on bipartite sparse random graphs. The model properties are compared to those of the p-clock model, in which planar continuous spins are discretized into p values. We test the goodness of the discrete approximation to XY spins used in numerical computations and simulations and its limits of convergence in given, p-dependent temperature regimes. The models are applied to describe the mode-locking transition of the phases of light modes in lasers at the critical lasing threshold. A frequency is assigned to each variable node, and function nodes implement a frequency matching condition. A nontrivial unmagnetized phase-locking occurs at the phase transition, where the frequency dependence of the phases turns out to be linear over a broad range of frequencies, as in a standard mode-locking multimode laser at the optical power threshold.