From Spin States to Social Consensus: Ising Approach to Dimer Configurations in Opinion Formation

The field of opinion dynamics has evolved steadily since the earliest studies applying magnetic physics methods to better understand social opinion formation. However, in the real world, complete agreement of opinions is rare, and biaxial consensus, especially on social issues, is rare. To address this challenge, Ishii and Kawabata (2018) proposed an extended version of the Bounded Confidence Model that introduces new parameters indicating dissent and distrust, as well as the influence of mass media. Their model aimed to capture more realistic social opinion dynamics by introducing coefficients representing the degree of trust and distrust, rather than assuming convergence of opinions. In this paper, we propose a new approach to opinion dynamics based on this Trust-Distrust Model (TDM), applying the dimer allocation and Ising model. Our goal is to explore how the interaction between trust and distrust affects social opinion formation. In particular, we analyze through mathematical models how various external stimuli, such as mass media, third-party opinions, and economic and political factors, affect people's opinions. Our approach is to mathematically represent the dynamics of trust and distrust, which traditional models have not addressed. This theoretical framework provides new insights into the polarization of opinions, the process of consensus building, and how these are reflected in social behavior. In addition to developing the theoretical framework by applying the dimer configuration, the dimer model and the Ising model, this paper uses numerical simulations to show how the proposed model applies to actual social opinion formation. This research aims to contribute to a deeper understanding of social opinion formation by providing new perspectives in the fields of social science, physics, and computational modeling.