“Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. Here we review the state of the art by focusing on a wide list of topics ranging from opinion, cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, social spreading. We highlight the connections between these problems and other, more traditional, topics of statistical physics. We also emphasize the comparison of model results with empirical data from social systems.”

“Finally, a word about finite size effects. The very concept of order-disorder phase-transitions is rigorously defined only in the limit of a system with an infinite number of particles (thermodynamic limit), because only in that limit truly singular behavior can arise. Social systems are generally composed by a large number N of agents, but by far smaller than the number of atoms or molecules in a physical system. The finiteness of N must play therefore a crucial role in the analysis of models of social dynamics (Toral and Tessone, 2007). Studying what happens when N changes and even considering the large-N limit is generally very useful, because it helps characterizing well qualitative behaviors, understanding which features are robust, and filtering out non-universal microscopical details.”