论文标题
2D添加剂小世界网络上的非平衡iSing模型
Non-equilibrium Ising Model on a 2D Additive Small-World Network
论文作者
论文摘要
在这项工作中，我们在二维添加剂小世界网络（A-SWN）上研究了ISING模型。系统模型由$ l \ times l $ square晶格组成，其中晶格的每个位点都被一个旋转变量占据，该旋转变量与最近的邻居旋转相互作用，并且具有一定的概率$ p $，可以随机连接到其更远的邻居之一。系统中存在的动态可以由在给定温度$ t $接触的概率$ q $来定义，同时，由于$ 1-Q $的概率，系统会在系统中遇到外部能量通量。与热浴的接触是根据大都市处方模拟的，通过一旋式翻转，而能量的输入则通过两旋式翻转工艺模仿，涉及一对相邻的旋转的同时翻转。我们已经采用了蒙特卡洛模拟来获得系统的热力学数量，例如，总计$ \ textrm {m} _ {\ textrm {\ textrm {l}}}^{\ textrm {f}}} $和交错$ \ textrm {m}每个自旋的磁化，易感性$χ_ {\ textrm {l}} $，以及减少的第四阶生命活页夹累积$ \ textrm {u} _ {\ textrm {l}}} $。我们已经在平面$ t $与$ q $的模型的固定状态下构建了相图，显示了$ p $的每个值的两个连续过渡线的存在：铁磁$ f $和promagagnetic $ p $阶段之间的一条线，以及$ p $ p $ and antifermagnetic $ p $ p $ p $ p $ p $ p $。因此，我们已经表明，当$ p $增加时，相图拓扑会发生变化。使用有限尺寸的缩放分析，我们还获得了系统的关键指数，其中有参数$ p $，我们已经观察到与常规平方晶格中的Ising模型到A-SWN的不同通用类别。
In this work, we have studied the Ising model with one- and two-spin flip competing dynamics on a two-dimensional additive small-world network (A-SWN). The system model consists of a $L\times L$ square lattice where each site of the lattice is occupied by a spin variable that interacts with the nearest neighbor spins and it has a certain probability $p$ of being additionally connected at random to one of its farther neighbors. The dynamics present in the system can be defined by the probability $q$ of being in contact with a heat bath at a given temperature $T$ and, at the same time, with a probability of $1-q$ the system is subjected to an external flux of energy into the system. The contact with the heat bath is simulated by one-spin flip according to the Metropolis prescription, while the input of energy is mimicked by the two-spin flip process, involving a simultaneous flipping of a pair of neighboring spins. We have employed Monte Carlo simulations to obtain the thermodynamic quantities of the system, such as, the total $\textrm{m}_{\textrm{L}}^{\textrm{F}}$ and staggered $\textrm{m}_{\textrm{L}}^{\textrm{AF}}$ magnetizations per spin, the susceptibility $χ_{\textrm{L}}$, and the reduced fourth-order Binder cumulant $\textrm{U}_{\textrm{L}}$. We have built the phase diagram for the stationary states of the model in the plane $T$ versus $q$, showing the existence of two continuous transition lines for each value of $p$: one line between the ferromagnetic $F$ and paramagnetic $P$ phases, and the other line between the $P$ and antiferromagnetic $AF$ phases. Therefore, we have shown that the phase diagram topology changes when $p$ increases. Using the finite-size scaling analysis, we also obtained the critical exponents for the system, where varying the parameter $p$, we have observed a different universality class from the Ising model in the regular square lattice to the A-SWN.
