竞争平衡模型对外场的响应
Response of the competitive balance model to the external field
AI总结：
本文通过平均场解析与蒙特卡洛模拟研究竞争平衡模型在外场作用下的演化，揭示系统随温度呈现顺磁或铁磁响应、铁磁滞后及磁化率遵循居里定律等行为。
摘要：
竞争平衡模型是作为结构平衡理论的扩展而提出的，旨在解释现实世界网络中观察到的异质性。在该模型中，不同的范式导致形成不同的友谊与敌意。例如，国家之间的友谊或敌意可能具有政治或宗教基础。所建议的哈密顿量在范式之间是对称的。我们的分析表明，只要一种范式在网络中占主导地位，就可以达到平衡状态，而范式转变只有通过施加外场才可能实现。在本文中，我们研究了外场对网络演化的影响。我们推导了该模型的平均场解，并通过执行蒙特卡洛模拟验证了解析解的准确性。我们观察到外场打破了系统的对称性。系统对该外场的响应取决于温度，可以是顺磁性的，也可以是铁磁性的。我们在铁磁区域中观察到了滞后行为。一旦社区基于某种范式形成，它们就会抵制变化。我们发现，为了避免浪费能量，我们需要了解网络中的随机行为水平。与磁系统类似，我们观察到磁化率遵循居里定律。
英文摘要：
The competitive balance model was proposed as an extension of the structural balance theory, aiming to account for heterogeneities observed in real-world networks. In this model, different paradigms lead to form different friendship and enmity. As an example, friendship or enmity between countries can have a political or religious basis. The suggested Hamiltonian is symmetrical between paradigms. Our analyses show that a balanced state can be achieved if just one paradigm prevails in the network and the paradigm shift is possible only by imposing an external field. In this paper, we investigate the influence of the external field on the evolution of the network. We drive the mean-field solutions of the model and verify the accuracy of our analytical solutions by performing Monte-Carlo simulations. We observe that the external field breaks the symmetry of the system. The response of the system to this external field, contingent upon temperature, can be either paramagnetic or ferromagnetic. We observed a hysteresis behavior in the ferromagnetic regime. Once communities are formed based on a certain paradigm, then they resist change. We found that to avoid wasting energy we need to know the level of stochastic behavior in the network. Analogous to magnetic systems, we observe that susceptibility adheres to Curie's law.
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