Thermodynamics of trajectories of the one-dimensional Ising model

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 1$d$ Ising model relate to the equilibrium ones of the 2$d$ Ising model. For Kawasaki dynamics we find a much simple dynamical phase structure, with transitions reminiscent of those seen in kinetically constrained models.Comment: 23 pages, 10 figure

Non-equilibrium Characterization of Spinodal Points using Short Time Dynamics

Though intuitively appealing, the concept of spinodal is rigourously defined only in systems with infinite range interactions (mean field systems). In short-range systems, a pseudo-spinodal can be defined by extrapolation of metastable measurements, but the point itself is not reachable because it lies beyond the metastability limit. In this work we show that a sensible definition of spinodal points can be obtained through the short time dynamical behavior of the system deep inside the metastable phase, by looking for a point where the system shows critical behavior. We show that spinodal points obtained by this method agree both with the thermodynamical spinodal point in mean field systems and with the pseudo-spinodal point obtained by extrapolation of meta-equilibrium behavior in short range systems. With this definition, a practical determination can be achieved without regard for equilibration issues.Comment: 10 pages, 12 figure

Numerical study of the evaporation/condensation phase transition of droplets for an irreversible reaction model

The ZGB model (Zif