2009/10/14 by Elena Agliari, Agliari, Elena, Adriano Barra +5
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #FOS: Physical sciences #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph)
paper · pdf · doi:10.48550/arxiv.0910.2470
openalex publication_date 2009/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we develop a theory for agents interactions on random graph. Our approach is based on describing a social network as a graph whose nodes represent agents and links between two of them stand for a reciprocal interaction. Each agent has to choose among a dichotomic option (i.e. agree or disagree) with respect to a given matter and he is driven by external influences (as media) and peer to peer interactions. These mimic the imitative behavior of the collectivity and may possibly be zero if the two nodes are disconnected. For this scenario we work out both the dynamics and the corresponding equilibria (statics). Once the 2-body theory is completely explored, we analyze, on the same random graph, a "diffusive strategic dynamics" with pairwise interactions, where detailed balance constraint is relaxed. The dynamic encodes some relevant processes which are expected to play a crucial role in the approach to equilibrium in social systems, i.e. diffusion of information and strategic choices. We observe numerically that such a dynamics reaches a well defined steady state that fulfills a "shift property": the critical interaction strength for the phase transition is lower with respect to the one expected from canonical equilibrium. Finally, we show how the stationary states obtained with this dynamics can be described by statistical mechanics equilibria of a diluted p-spin model, for a suitable non-integer real p>2. Several implications from a sociological perspective are discussed together with some general outlooks.