Out of equilibrium Ising spin dynamics on sparse networks

by Eduardo Dominguez Vazquez (University of Havana, Cuba)

Tuesday 24 May 2016, 13:30 → 14:30 Europe/Stockholm

132:028

The time evolution of the joint probability distribution for systems with a large number of interacting spins is typically explored by means of very expensive stochastic simulations. In this work, two alternative treatments are discussed for the discrete and continuous time dynamics on random sparse networks. The main advantage of these proposals is that, in some cases, reasonably accurate approximations can be obtained for the time dependence of quantities like local magnetizations and correlations with much less computational effort than the standard Monte Carlo Markov Chain approach. The discrete-time analysis is based on the minimization of a generalized functional with a structure that resembles a variational free energy of the full probability distribution. On the other hand, the continuous-time scenario is studied in the context of a "random point process" formalism. This approach allowed for a generalization of the dynamic cavity method, which was previously derived for the discrete-time case. An important feature of both approximations is to exploit the tree-like structure of sparse networks to simplify the form of the full probability distribution.