A simple mean field model for social interactions: dynamics, fluctuations, criticality
نویسندگان
چکیده
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in the limit of infinitely many interacting individuals, and show that phase transition occurs. Then, after having obtained the dynamics of normal fluctuations around this limit, we analyze long time fluctuations for critical values of the parameters. We show that random inhomogeneities produce critical fluctuations at a shorter time scale compared to the homogeneous system.
منابع مشابه
Dynamics of condensation in zero-range processes
The dynamics of a class of zero-range processes exhibiting a condensation transition in the stationary state is studied. The system evolves in time starting from a random disordered initial condition. The analytical study of the large-time behaviour of the system in its mean-field geometry provides a guide for the numerical study of the one-dimensional version of the model. Most qualitative fea...
متن کاملNonequilibrium Dynamics of the Zeta Urn Model
We consider a mean-field dynamical urn model, defined by rules which give the rate at which a ball is drawn from an urn and put in another one, chosen amongst an assembly. At equilibrium, this model possesses a fluid and a condensed phase, separated by a critical line. We present an analytical study of the nonequilibrium properties of the fluctuating number of balls in a given urn, considering ...
متن کاملChapter 6 . Criticality and Isostaticity in Fiber Networks
It has been known since Maxwell that collections of particles interacting via central forces only become rigid above the isostatic threshold, where the constraints and internal degrees of freedom just balance [1,2]. However, such networks can be stabilized below this threshold by additional interactions [3–5]. Here we elucidate the relative roles of bending versus central force interactions in ...
متن کاملStructural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches.
Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanis...
متن کاملScaling in cognitive performance reflects multiplicative multifractal cascade dynamics
Self-organized criticality purports to build multi-scaled structures out of local interactions. Evidence of scaling in various domains of biology may be more generally understood to reflect multiplicative interactions weaving together many disparate scales. The self-similarity of power-law scaling entails homogeneity: fluctuations distribute themselves similarly across many spatial and temporal...
متن کامل