Thermodynamics of trajectories of the 1D-Ising model

E. S. LOSCAR; J. P. GARRAHAN

Ciudad autónoma de Buenos Aires

Workshop; Structure and Dynamics of Glassy, Supercooled and Nanoconfined Fluids 2012; 2012

CONEA, INQUIMAE. Facultad de Cinecias Exactas y Naturales UBA

We present a numerical study of the dynamics of the one-dimensional Ising model by applying the large-deviation method to describe ensembles of dynamical trajectories.  In this approach trajectories are classified according to a dynamical order parameter and the structure of ensembles of trajectories can be understood from the properties of large-deviation functions, which play the role of dynamical free-energies. We consider both Glauber and Kawasaki dynamics, and also the presence of a magnetic field.  For Glauber dynamics in the absence of a field we confirm the analytic predictions of Jack and Sollich about the existence of critical dynamical, or space-time, phase transitions at critical values of the ``counting´´ field s.  In the presence of a magnetic field the dynamical phase diagram also displays first order transition surfaces. We discuss how these non-equilibrium transitions in the 1d Ising model relate to the equilibrium ones of the 2d Ising model.  For Kawasaki dynamic we find a much simple dynamical phase structure, with transitions reminiscent of those seen in kinetically constrained models.