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

Pawat Akara-pipattana1, Sergei Nechaev1,2, and Bogdan Slavov*,†

  • *Independent researcher.
  • †Contact author: slavovbog@gmail.com
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Phys. Rev. E 114, 024107 – Published 3 August, 2026

DOI: https://doi.org/10.1103/ptty-5zxd

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.

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Phys. Rev. E 114, 024107– Published 3 August, 2026
  • Received 25 November 2025
  • Revised 29 May 2026
  • Accepted 29 June 2026
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