In this article, we have employed Monte Carlo simulations to study the Ising model 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 for a spin variable that interacts with the nearest neighbor and has a certain probability p of being additionally connected at random to one of its farther neighbors. The system is in contact with a heat bath at a given temperature T and it is simulated by one-spin flip according to the Metropolis prescription. We have calculated the thermodynamic quantities of the system, such as the magnetization per spin \(m_{L}\), magnetic susceptibility \(\chi _{L}\), and the reduced fourth-order Binder cumulant \(U_{L}\) as a function of T for several values of lattice size L and additive probability p. We also have constructed the phase diagram for the equilibrium states of the model in the plane T versus p showing the existence of a continuous transition line between the ferromagnetic F and paramagnetic P phases. Using the finite-size scaling (FSS) theory, we have obtained the critical exponents for the system, where varying the parameter p, we have observed a change in the critical behavior from the regular square lattice Ising model to A-SWN.

在本文中，我们使用蒙特卡罗模拟来研究二维加性小世界网络 (A-SWN) 上的 Ising 模型。该系统模型由一个\(L\times L\)方格组成，其中格的每个位置都被一个自旋变量占据，该自旋变量与最近的邻居相互作用，并且有一定的概率p额外随机连接到它的一个更远的邻居。该系统与给定温度T的热浴接触，并根据 Metropolis 规定通过单次翻转来模拟。我们已经计算了系统的热力学量，例如每个自旋的磁化强度\(m_{L}\)、磁化率\(\chi _{L}\) ，以及作为T的函数的约简四阶 Binder 累积量\(U_{L}\) ，用于多个晶格大小L和加性概率p的值。我们还构建了模型在平面T与p中的平衡状态的相图，显示铁磁F和顺磁P相之间存在连续过渡线。使用有限尺寸缩放 (FSS) 理论，我们获得了系统的临界指数，其中改变参数p，我们观察到从规则方格 Ising 模型到 A-SWN 的临界行为发生了变化。