Collective communication in a transparent world: Phase transitions in a many-body Potts model and a social-quantum correspondence.

Abstract

Digitally connected societies approach a "transparent" regime where all agents can interact without geographic or social barriers-a limit realized by complete graph topologies. We construct a mean-field theory of a q-state Potts model with many-body interactions on this geometry, modeling agents from q distinct communities. Analyzing the illustrative case of competing pairwise and three-body couplings, we identify three equilibrium phases in the thermodynamic limit: symmetric (all communities equal), reduced symmetry (q-1 communities surviving), and consensus (one dominant group). For two-community systems, we identify a special coupling regime where the influence of interactions cancels out, yielding purely entropy-driven dynamics-a statistical physics representation of atomized societies without structured influence. Monte Carlo simulations confirm these regimes and reveal metastable switching dynamics in finite systems. Furthermore, we establish a correspondence (q↔N) between this model and a mean-field SU(N) quantum spin system with quadratic and cubic interactions. This "social-quantum" correspondence suggests a representation-theoretic description for classifying symmetry-broken macrostates and offers an interpretive link between quantum mean-field phase structure and opinion stratification.