Understanding the effects of disordered interactions using dynamic mean field theory

by Dr Joseph Baron (IFISC, Spain)

Monday 15 Nov 2021, 15:45 → 17:45 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

hybrid mode.

 

zoom link :  https://stockholmuniversity.zoom.us/j/622224375

 

There exist many examples of systems that consist of a large number individual components that interact with one another in a heterogeneous (or disordered) manner. Such systems include spin glasses, complex ecosystems, neural networks and social networks. Dynamic mean field theory (DMFT) is an elegant tool from Statistical Physics that allows one to deduce the collective behaviour of the system as a whole, given only statistical information about the interactions between components. This is done by treating the large-scale system as a thermal bath with which each individual component interacts. Using DMFT, one can deduce the statistical behaviour of the individual components self-consistently and build an understanding of the kinds of “phase transitions” that occur in the system in question.

I will present two examples. Firstly, I will introduce a model of opinion dynamics in which each individual interacts heterogeneously with its neighbours. Using DMFT, I will show how consensus, polarisation and a coexistence of opinion can all occur within this model and under what circumstances. Secondly, I will discuss a paradigmatic model of complex ecosystems (the generalised Lotka-Volterra system). In the case where the model ecosystem reaches a stable steady state (after the extinction of some species), I will demonstrate how the interaction statistics of the surviving community differ from those of the original and what this implies for ecosystem stability.