How can we reach consensus? The answer from the micro-configurations of a 2-D Ising model

Abstract

We study opinion formation by uncovering the relevant aspects hiding in the distribution of micro-configurations in a 2-D Ising model. The external field denotes the external influence such as guiding viewpoint, and temperature represents randomness of the agents. The full-positive configuration or the full-negative configuration means consensus. We find that the probability of the full-positive configuration and the full-negative configuration can reach [Formula: see text] (which implies the equal splitting of a group) if the interaction is strong enough and the system is free from external field; the probability of the full-positive configuration can reach 1 (which means consensus) if the positive external field is strong enough under condition of given interaction and temperature. These phenomena are regarded as the reversing mechanism of the full-negative configuration induced by the external field — an opinion reversal. The equal splitting and consensus can be broken down as temperature rises. We discuss the dependence of interaction strength [Formula: see text] (with which the equal splitting occurs) on temperature [Formula: see text], the dependence of external field strength [Formula: see text] (with which the consensus occurs) on interaction strength [Formula: see text] at a certain temperature, as well as the scaling relations responsible for the probability of the full-negative configuration varying with temperature under different conditions. The findings provide us with a good description to understand opinion formation.