A veritable zoology of successive phase transitions in the asymmetric q-voter model on multiplex networks
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 q1 and q2. 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).