2016/08/26 by Opoku, Alex A., Edusei, Kwame Owusu, Ansah, Richard
#FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.1608.07363
This paper proposes a conditional Curie-Weiss model as a model for opinion formation in a society polarized along two opinions, say opinions 1 and 2. The model comes with interaction strength β>0 and bais h. Here the population in question is divided into three main groups, namely: Group one consisting of individuals who have decided on opinion 1. Let the proportion of this group be given by s. Group two consisting of individauls who have chosen opinion 2. Let r be their proportion. Group three consisting of individuals who are yet to decide and they will decide based on their environmental conditions. Let 1-s-r be the proportion of this group. We show that the specific magnetization of the associated conditional Curie-Weiss model has a first order phase transition (discontinuous jump in specific magnetization) at β^*=(1-s-r)-1. It is also shown that not all the discontinuous jumps in magnetization will result in phase change. We point out how an extention of this model could serve as a random field Curie-Weiss model where the random field distribution has nonvanishing mean.