Q-Neighbor Ising model on random networks

Abstract

A modified kinetic Ising model with Metropolis dynamics, so-called [Formula: see text]-neighbor Ising model, is investigated on random graphs. In this model, each spin interacts only with [Formula: see text] spins randomly chosen from its neighborhood. Investigations are performed by means of Monte Carlo (MC) simulations and the analytic pair approximation (PA). The range of parameters such as the size of the [Formula: see text]-neighborhood and the mean degree of nodes of the random graph is determined for which the model exhibits continuous or discontinuous ferromagnetic (FM) phase transition with decreasing temperature. It is also shown that, in the case of discontinuous transition for large enough and fixed mean degree of nodes, the width of the hysteresis loop oscillates with the parameter [Formula: see text], expanding for even and shrinking for odd values of [Formula: see text]. Predictions of the PA show satisfactory quantitative agreement with results of MC simulations.