Effective Interactions in Group Competition with Strategic Diffusive Dynamics

TL;DR

This paper investigates a non-equilibrium diffusive dynamics on random graphs, revealing a higher critical temperature for phase transition and connecting steady states to diluted p-spin models, with implications for physics and sociology.

Contribution

It introduces a novel diffusive strategic dynamics lacking detailed balance, showing its steady states relate to diluted p-spin models and differ from equilibrium predictions.

Findings

Critical temperature is higher than equilibrium predictions.

Steady states correspond to diluted p-spin model equilibria.

Dynamics reach a well-defined steady state without detailed balance.

Abstract

We analyze, on a random graph, a diffusive strategic dynamics with pairwise interactions, where nor Glauber prescription, neither detailed balance hold. We observe numerically that such a dynamics reaches a well defined steady state that fulfills a shift property: the critical temperature of the canonical ferromagnetic phase transition is higher with respect to the expected equilibrium one, known both numerically via Glauber relaxation or Monte Carlo simulations as well as analytically via cavity techniques or replica approaches. We show how the relaxed states of this kind of dynamics can be described by statistical mechanics equilibria of a diluted p-spin model, for a suitable non-integer real p. Several implications from both theoretical physics and quantitative sociology points of view are discussed.