Collective communication in a transparent world: Phase transitions in a many-body Potts model and social-quantum duality
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 solve exactly 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 key phases in the thermodynamic limit: democratic (all communities equal), marginalized (q-1 communities surviving), and consensus (one dominant group). For two-community systems, we identify a special coupling regime where interaction energies cancel, yielding purely entropy-driven dynamics -- a statistical physics representation of atomized societies without structured influence. Monte Carlo simulations confirm these phases and reveal metastable switching dynamics in finite systems. Furthermore, we establish an exact correspondence between this social model and mean-field SU(N) quantum spin systems with quadratic and cubic Casimir interactions, revealing a social-quantum duality. This duality enables quantitative classification of social structures via Young diagrams and reinterprets quantum symmetry breaking as opinion stratification, bridging statistical sociology and quantum many-body physics.
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