Phase transition and universality of the three-one spin interaction based on the majority-rule model

Abstract

In this work, we study the opinion dynamics of majority-rule model on a complete graph with additional social behavior namely anticonformity. We consider four spins with three-one interaction; three spins persuade the fourth spin in the population. We perform analytical and numerical calculations to find the critical behavior of the system. From both, we obtained the agreement results, e.g. the system undergoes a second-order phase transition and the critical point of the system only depends on the population number. In addition, the critical point decays exponentially as the number population increases. For the infinite population, the obtained critical point is [Formula: see text], which agrees well with that of the previous work. We also obtained the critical exponents [Formula: see text] and [Formula: see text] of the model, thus, the model is in the same universality class with the mean-field Ising.

The external field effect on the opinion formation based on the majority rule and the q-voter models on the complete graph

“…We find the critical point and the scaling parameters of both models using finite-size scaling relations in (4)- (5). We find that the critical point d c of the majority rule and q-voter models are d c ≈ 0.379 for p = 0.2 and d c ≈ 0.256 for p = 0.1, respectively.…”

“…Simple interaction on the microscopic level can present the macroscopic behavior such as phase transition phenomena. One of the reasons scholars study opinion dynamics models is that it presents statistical physics features such as order-disorder phase transitions, scaling, and universality [3,4,5,6].…”

Phase Transition in the Galam’s Majority-Rule Model with Information-Mediated Independence

“…In this model, random groups of agents are chosen, and after the interaction of such agents, all of them assume the initial majority opinion. The model was studied elsewhere [32][33][34][35][36][37][38][39], and it was applied to a series of practical problems, like antivax movement [40], USA [41] and French [42] presidential elections, and terrorism [43], among many others.…”