Presentacion mural: From microscopic to macroscopic dynamics in systems with two symmetric absorbing states

FEDERICO VAZQUEZ

Punta del Este

Conferencia; Medyfinol 2008; 2008

The field of interacting particle systems was born in the late 1960's,motivated by the study of non-equilibrium statistical mechanics.  Although,nowadays is formally consider as a branch of probability theory, physicistshave largely used these systems to analyze different stochastic  models, suchas the Ising model, neural networks, tumor growth, epidemic  spreading, etc.During the last decade special attention was given to systems with twosymmetric absorbing states, due to the emergence of a large amount of newmodels coming form researchers working in  interdisciplinary physics, such as,ecological modeling, opinion dynamics and  language evolution.  We present an approach to  study general spin models with two symmetricabsorbing states.  Starting from  the microscopic dynamics on a squarelattice, we derive a Langevin equation  for  the time evolution of themagnetization field, that successfully explains  coarsening properties of awide range of  nonlinear voter models and systems  with intermediate states.We find that the  macroscopic behavior only depends  on the first derivativesof the spin-flip probabilities.  Moreover, an  analysis of the  mean-fieldterm reveals the three types of transitions  commonly observed in thesesystems -generalized voter, Ising and directed  percolation-.  Monte Carlosimulations of the spin dynamics qualitatively  agree with theoreticalpredictions.