Is Independence Necessary for a Discontinuous Phase Transition within the q -Voter Model?

摘要

We ask a question about the possibility of a discontinuous phase transition and the related social hysteresis within the q -voter model with anticonformity. Previously, it was claimed that within the q -voter model the social hysteresis can emerge only because of an independent behavior, and for the model with anticonformity only continuous phase transitions are possible. However, this claim was derived from the model, in which the size of the influence group needed for the conformity was the same as the size of the group needed for the anticonformity. Here, we abandon this assumption on the equality of two types of social response and introduce the generalized model, in which the size of the influence group needed for the conformity q c and the size of the influence group needed for the anticonformity q a are independent variables and in general q c ≠ q a . We investigate the model on the complete graph, similarly as it was done for the original q -voter model with anticonformity, and we show that such a generalized model displays both types of phase transitions depending on parameters q c and q a .