A veritable zoology of successive phase transitions in the asymmetric $q$-voter model on multiplex networks

TL;DR

This paper investigates the complex phase transition behaviors of a nonlinear $q$-voter model with stochastic noise on multiplex networks, revealing multiple types of phase transitions including mixed-order, through simulations and analytical solutions.

Contribution

It introduces a study of phase transitions in a $q$-voter model with different lobby sizes on each network level, uncovering successive and hybrid phase transitions.

Findings

Identification of successive phase transitions depending on parameters.

Discovery of mixed-order (hybrid) phase transitions.

Analytical solutions supporting simulation results.

Abstract

We analyze a nonlinear $q$-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby $q$ (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The $q$-voter model has been applied on multiplex networks in a previous work [Phys. Rev E. 92. 052812. (2015)], and it has been shown that the character of the phase transition depends on the number of levels in the multiplex network as well as the value of $q$. Here we study phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters $q_1$ and $q_2$. We find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phases appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. We perform simulations and obtain supporting analytical solutions on a simple multiplex case - a duplex clique, which consists of two fully overlapped complete graphs (cliques).