Nonequilibrium phase transitions in a model with social influence of inflexible units

In many social, economical and biological systems, the evolution of the states of interacting units cannot be simply treated with a physical law in the realm of traditional statistical mechanics. We propose a simple binary-state model to discuss the effect of the inflexible units on the dynamical behavior of a social system, in which a unit may have a chance to keep its state with a probability 1 - q even though its state is different from those of the majority of its interacting neighbors. It is found that the effect of these inflexible units can lead to a nontrivial phase diagram.