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 ($q\leftrightarrow N$) between this model and a mean-field $SU\left(N\right)$ 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.

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• Classical statistical mechanics
• Phase diagrams
• Quantum phase transitions
• Social systems
• Social networks
• Exact solutions for many-body systems
• Potts model