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

Angelika Abramiuk,Katarzyna Sznajd-Weron,Jakub Pawłowski

doi:10.3390/e21050521

Angelika Abramiuk, Katarzyna Sznajd-Weron + Show 1 more

Open Access

https://doi.org/10.3390/e21050521

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Abstract

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 and the size of the influence group needed for the anticonformity are independent variables and in general . 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 and .

Highlights

There has been an increased interest in discontinuous phase transitions in models of opinion dynamics [1,2,3,4,5,6]
The main reason for this interest may be the observation of the social hysteresis, which appears only in the case of discontinuous phase transitions
It has occurred that discontinuous phase transitions are not that typical in models of opinion dynamics, especially if we consider models belonging to the class of the binary-state dynamics [13,14] such as the voter model [15], the majority-vote model [15,16,17], the Galam model [18], the Sznajd model [19], the threshold model [6,20], the q-voter model [21] or the threshold q-voter model [22,23]

Summary

Introduction

There has been an increased interest in discontinuous phase transitions in models of opinion dynamics [1,2,3,4,5,6]. It was only the inertia, introduced on the microscopic level into the majority-vote model, that has changed the type of the phase transition from a continuous to a discontinuous one [2,4] This result, might be criticized by the classicism of. The original q-voter model with anticonformity has been investigated exclusively on a complete graph, so this structure is the best for the comparison with the previous results For this structure analytical calculations are simple, and it is possible to derive exact analytical formula for the critical point below which an up-down (yes-no) symmetry is broken, as well as the tricritical point above which the phase transition becomes discontinuous. The second possibility has been confirmed by social experiments [37] and we formulated the version without repetitions

Results

Time Evolution

Stationary States

Landau Approach for Continuous and Discontinuous Phase Transitions

Application of the Landau Approach

Conclusions