Non-equilibrium kinetic Biswas–Chatterjee–Sen model on complex networks

Abstract

The phase transition of a discrete version of the non-equilibrium Biswas–Chatterjee–Sen model, defined on Erdös–Rényi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs), has been studied. The mutual interactions (or affinities) can be both positive and negative, depending on the noise parameter value. Through extensive Monte Carlo simulations and finite-size scaling analysis, the continuous phase transitions and the corresponding critical exponent ratios have been obtained for several values of the average connectivity z. The effective dimensionality of the system has been found to be Deff≈1.0 for all values of z, which is similar to the one obtained on Barabási–Albert networks. The present results show that kinetic models of discrete opinion dynamics belong to a different universality class as the corresponding equilibrium Ising and Potts, and non-equilibrium majority-vote models on the same ERRGs and DERRGs. It is also noticed that the kinetic model here studied on ERRGs and DERRGs is in different universality classes for connectivities z<20, while for z≥20 the critical exponents are the same for both random graphs.