中文摘要：

文中基于Newman-Watts（NW）小世界复杂网络模型,提出复杂网络上具有长程相互作用的XY转子模型。通过对复杂网络上XY转子系统的序参量M和温度T的数值计算,研究系统在不同的转子平均能量U下具有的热力学行为,发现在小世界复杂网络上的长程相互作用系统呈现二级相变;通过计算系统动量的自关联函数,结果显示系统在不同相具有不同相关特性;通过对系统最大Lyapunov指数的计算,结果表明在小世界复杂网络上的长程相互作用XY转子系统呈现出混沌特性。

英文摘要：

Based on Newman-Watts（ NW） small-world network,XY rotors model with long-range interaction via randomedge-adding on complex network is constructed. Using the symplectic integration,the thermodynamic behavior of the order parameter M and the temperature T of the XY rotorssystem under different total energy density U are obtained. Results show the second-order phase transition from uniform phase to clustering one occurs depending on the probability of random edgeadding. The auto-correlation of momenta reveals the different correlative characteristics in the region of uniform phase and clustering one. Moreover,calculation of the largest Lyapunov exponent shows the chaotic characteristic of the long-range interaction system on the small-worldnetwork. A peak of the largest Lyapunov exponent near critical point appeared depending on the probability of random edge-adding.