Disorder induced phase transition in kinetic models of opinion dynamics

We propose a model of continuous opinion dynamics, where mutual interactions can be both positive and negative. Different types of distributions for the interactions, all characterized by a single parameter $p$ denoting the fraction of negative interactions, are considered. Results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p=p_c below which a consensus is reached. Although the order-disorder transition is analogous to a ferromagnetic-paramagnetic phase transition with comparable critical exponents, the model is characterized by some distinctive features relevant to a social system.

💡 Research Summary

The paper introduces a kinetic model of continuous opinion dynamics in which pairwise interactions can be either positive or negative. Each agent i holds an opinion o_i(t) bounded between –1 and 1, and at each time step the opinion updates according to o_i(t+1)=o_i(t)+μ_{ij} o_j(t), where μ_{ij} is a real interaction strength. The fraction p of negative μ_{ij} values is the control parameter: increasing p introduces more “disagreement” into the system. The model is defined on a fully connected network (infinite range), and μ_{ij} are taken as annealed random variables drawn anew at every interaction. Two families of μ_{ij} distributions are studied: (i) a continuous uniform distribution in