Ising Models of Social Impact: the Role of Cumulative Advantage

Abstract
A statistical mechanical model for Latané's theory of social impact is discussed and extended to include learning. When the persuasive and supportive strengths are not equal, a ferromagnetic and a spin-glass phase emerge. When the persuasive and supportive strengths are equal, and a cumulative advantage learning scheme is used, then the model exhibits two ferromagnetic phases distinguishable by the structure of the correlations. In the first phase the correlations are normally distributed. In the second phase all elements are shown to be highly correlated with either a single element or a small number of elements. These "leaders" determine the equilibrium state of the system.