Statistical-physics methods applied to social systems: voter / Sznajd / Galam majority-rule / Deffuant bounded-confidence / Axelrod culture; agent-based modeling; phase transitions in opinion dynamics; Schelling segregation;…
Sociophysics
Galam sociophysics foundations
Galam 1982-2008: introduced statistical-physics framework for opinion dynamics; uses Ising-like models, kinetic-theory, percolation to…
Sznajd opinion model
Sznajd-Weron 2000: 1D rule pair-of-aligned-neighbors converts neighbors; phase transition at p=1/2 in mean-field; key minimal model of…
Agent-based social models
Schelling 1971 segregation, Axelrod 1997 culture, Epstein-Axtell 1996 Sugarscape; bottom-up emergence of macro patterns from local rules;…
Voter model (Clifford-Sudbury)
Clifford-Sudbury 1973 / Holley-Liggett 1975: each agent adopts random neighbor's state; consensus time scales as N ln N on complete graph…
Social network physics
Watts-Strogatz 1998 small-world, Barabasi-Albert 1999 scale-free; degree-distribution heavy-tail; spreading of behaviors and information…
Schelling segregation
Schelling 1971: even mild same-color preference (above 30 percent) causes spatial segregation in agent-based simulation; classic…
Bounded-confidence (Deffuant / Hegselmann-Krause)
Deffuant 2000 and Hegselmann-Krause 2002: continuous opinion in [0,1]; agents only interact with others within confidence threshold…
Majority-rule (Galam)
Galam 1986/2008: random-group majority-rule reproduces minority-spreading and tie-breaking by inertia; predicts referendum outcomes (e.g.…
Axelrod culture dissemination
Axelrod 1997: vector-of-cultural-traits + similarity-driven interaction yields polarization or homogenization phase transition tunable by…
Social impact theory (Latane)
Latane 1981: I = f(S) g(I) h(N) - strength, immediacy, number determine social influence; cellular-automaton implementation produces…
Phase transitions in opinion dynamics
Order-disorder transitions in Ising-like opinion models; critical exponents match 2D Ising universality class for some variants;…
Social temperature and fluctuation
Effective temperature parameterizes random behavior versus rational choice; fluctuation-dissipation analogues relate response-to-shock and…
Kinetic Boltzmann opinion (Toscani)
Toscani 2006 Boltzmann-type kinetic equation for opinion: f_t = collision-integral with binary-interaction kernels; continuous-opinion…
Galam rumor-spreading (minority spreading)
Galam 2002: minority opinion (e.g., conspiracy theory) can spread via majority-rule discussion in groups when there's tie-breaking inertia…
Castellano statistical physics of social dynamics
Castellano-Fortunato-Loreto 2009 review: applies tools of statistical physics (phase transitions / scaling / RG) to social phenomena:…
Sznajd extension + ABM modifications
Stauffer 2000s extended Sznajd to 2D, 3D, scale-free networks; introduces external-field bias; ferromagnetic-like consensus formation;…
Percolation opinion spread
Watts 2002 / Centola 2010 complex-contagion on networks: opinion only spreads via multiple-source reinforcement (vs simple-contagion…
Twitter / X cascade spread (empirical)
Vosoughi-Roy-Aral 2018 Science: false news spreads ~6x faster + farther on Twitter than true news; novelty + emotional content drive…
Galam (1982)
S Galam 1982 + 2008 'Sociophysics' opinion-dynamics; modern modern foundational text + 2024 misinformation-spread + LLM-content moderation…
Voter model (Clifford-Sudbury 1973)
P Clifford-A Sudbury 1973 voter-model; modern modern foundational text + 2024 multilayer-voter coupled-political-LLM influence networks.
Schelling segregation (1971)
T Schelling 1971 (Nobel 2005) + 1978 segregation-model; modern modern foundational text + 2024 agent-based ML-residential land-use…
Ising opinion (Galam-Moscovici 1991)
S Galam-S Moscovici 1991 + Sznajd 2000 ising-opinion-model; modern modern foundational text + 2024 q-voter + Deffuant + threshold-models…
Zipf (1949)
G Zipf 1949 'Human Behavior and the Principle of Least Effort'; modern modern foundational + 1999 Mandelbrot + 2024 LLM-token-frequency…
Pareto (1897)
V Pareto 1897 + 1965 P(W>w) ~ w^-α power-law income; modern modern foundational text + 2024 wealth-inequality global-wealth-2024 report.