Thermodynamics of trajectories of the one-dimensional Ising model

• Autores: Loscar, Ernesto Selim; Mey, Antonia S. J. S.; Garrahan, Juan P.
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Classical Monte Carlo simulations; Classical phase transitions (Theory); Finite-size scaling; Phase diagrams (Theory)
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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 dynamics we find a much simple dynamical phase structure, with transitions reminiscent of those seen in kinetically constrained models.
Fil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. University of Nottingham; Estados Unidos
Fil: Mey, Antonia S. J. S.. University of Nottingham; Estados Unidos
Fil: Garrahan, Juan P.. University of Nottingham; Estados Unidos