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

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 0.5 (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 Jc (with which the equal splitting occurs) on temperature T, the dependence of external field strength Bc (with which the consensus occurs) on interaction strength J 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.