Abstract

The q-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model for the opinion formation in which the agents, represented by two-state spins, change their opinions according to a Metropolis-like algorithm taking into account interactions with only a randomly chosen subset of their q neighbors. Depending on the model parameters in Monte Carlo simulations, phase diagrams are observed with first-order ferromagnetic transition, both first- and second-order ferromagnetic transitions and second-order ferromagnetic and spin-glass-like transitions as the temperature and fraction of antiferromagnetic exchange integrals are varied; in the latter case, the obtained phase diagrams qualitatively resemble those for the dilute spin-glass model. Homogeneous mean-field and pair approximations are extended to take into account the effect of the antiferromagnetic exchange interactions on the ferromagnetic phase transition in the model. For a broad range of parameters, critical temperatures for the first- or second-order ferromagnetic transition predicted by the homogeneous pair approximation show quantitative agreement with those obtained from Monte Carlo simulations; significant differences occur mainly in the vicinity of the tricritical point in which the critical lines for the second-order ferromagnetic and spin-glass-like transitions meet.

Graphic abstract

中文翻译：

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q邻居伊辛模型中随机图上的铁磁和自旋玻璃状跃迁

摘要

的q -neighbor伊辛模型上均匀随机图进行了研究与反铁磁交换积分和与铁磁那些其余边缘随机相关联的边缘的一小部分。这是一种非均衡的意见形成模型，其中，以两态自旋表示的主体根据类似于Metropolis的算法，仅考虑与q的随机选择子集之间的相互作用，来更改其看法邻居。根据蒙特卡洛模拟中的模型参数，观察到一阶铁磁跃迁，一阶和二阶铁磁跃迁以及二阶铁磁和类似自旋玻璃的跃迁作为温度和反铁磁交换分数的相图。积分是多种多样的；在后一种情况下，获得的相图在质量上类似于稀旋转玻璃模型的相图。扩展了均值均值和对近似，以考虑反铁磁交换相互作用对模型中铁磁相变的影响。对于广泛的参数，均质对近似预测的一阶或二阶铁磁跃迁的临界温度与从蒙特卡洛模拟获得的临界温度显示出定量的一致性；显着差异主要发生在三临界点附近，在该临界点处，二阶铁磁和类自旋玻璃跃迁的临界线相交。

图形摘要