Thermodynamics of trajectories of the one-dimensional Ising model

Details Thermodynamics of trajectories of the one-dimensional Ising model Thermodynamics of trajectories of the one-dimensional Ising model

2011-10-21

arxiv.org/abs/1110.4857v1

Journal of Statistical Mechanics: Theory and Experiment, (2011) P12011

Physics

Condensed Matter

Statistical Mechanics

23 pages, 10 figures

Scientific paper

10.1088/1742-5468/2011/12/P12011

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.

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