A Sociological Model of Political Regimes in the Parisi–Talagrand and Sherrington–Kirkpatrick Framework: Imposed vs. Natural Replica Symmetry in Totalitarian Systems

This study proposes a theoretical–empirical framework for analyzing political regimes based on a structural analogy between electoral behavior and spin-glass systems in statistical physics. Society is modeled as a system of interacting agents (voters) influenced by both interpersonal interactions and external factors such as media and institutions, formalized through a social Hamiltonian. By introducing a partition function and free energy, political regimes are interpreted as distinct macroscopic phases governed by four effective macro-parameters: external field, conformism, interaction heterogeneity, and inverse social temperature. Democratic societies correspond to a multistable regime characterized by sensitivity to initial conditions and replica symmetry breaking (RSB), reflecting the coexistence of competing social configurations. Authoritarian regimes, in contrast, arise when a strong unidirectional external field, high conformism, and low effective social temperature stabilize a single dominant macroscopic state, producing a regime analogous to replica symmetry (RS). A central result of the model is the distinction between the predictability of macroscopic outcomes and structural social multistability, as well as between natural and externally imposed homogenization of collective behavior. To illustrate the empirical relevance of the framework, the model is applied to the transition from the Weimar Republic to the National Socialist regime (1919–1933), using aggregated electoral data to construct proxy indicators for the effective parameters governing social interactions. The proposed approach enables structural identification of early signals of authoritarian transition through changes in the parameters of social dynamics.