We build simple computational models of belief dynamics within the framework of discrete-spin statistical physics models, and explore how suitable they are for understanding and predicting real-world belief change on both the individual and group levels. We find that accurate modeling of real-world patterns requires attending to social interaction rules that people use, network structures in which they are embedded, distributions of initial beliefs and intrinsic preferences, and the relative importance of social information and intrinsic preferences. We demonstrate that these model parameters can be constrained by empirical measurement, and the resulting models can be used to investigate the mechanisms underlying belief dynamics in actual societies. We use data from two longitudinal studies of belief change, one on 80~individuals living in an MIT dorm during the 2008 presidential election season, and another on 94~participants recruited from Mechanical Turk during the 2016 presidential election primary season. We find that simple statistical physics-based models contain predictive value for real-world belief dynamics and enable empirical tests of different assumptions about the underlying network structure and the social interaction rules.