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
Highlights
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
For the majority vote model on random graphs, phase diagram is obtained resembling qualitatively that for the equilibrium Ising model on random graphs which is a model for a dilute spin glass (SG) [42], with second-order transitions from the PM to the FM and SG phases and a tricritical point (TCP) in which critical lines corresponding to the two above-mentioned transitions meet [35]
The aim of this paper is to investigate the effect of symmetric AFM interactions between agents on phase transitions in a nonequilibrium model for the opinion formation in which both first- and second-order FM transitions are possible
Summary
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. The aim of this paper is to investigate the effect of symmetric AFM interactions between agents on phase transitions in a nonequilibrium model for the opinion formation in which both first- and second-order FM transitions are possible. For this purpose, the qneighbor Ising model on random graphs is studied which belongs to a family of nonequilibrium Ising models in which the spins in nodes and the edges of the network of interactions are in contact with thermal baths with different temperatures [25].
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