Transição de fase dinâmica em modelos de spins

Abstract

In this paper we investigate the phase diagram of the static and dynamic models of spins, with random field Ising with a bimodal probability distribution, Blume-Capel and Blume- Capel with oscillating external field, using the mean field approximation (MFA) and the effective field (EFT). The thermal properties of balance are theoretically obtained via the mathematical formalism of statistical mechanics of Boltzmann and Gibbs. The stationary states of the kinetic models are described by the stochastic dynamics of Glauber. Using MFA show that the lines in balance first order obtained by Maxwell s construction for the free energy, and out of balance are different. To analyze the stability of sitema the Lyapunov exponent is calculated numerically. In this approach we found values distinct Hc(Dc) for the Ising model with random field (Blume-Capel), ie Hc (static) [Dc (static)] 6= Hc (dynamic) [Dc (dynamic)]. On the other hand, using EFT for first order lines also differ, but now we have Hc (static) [Dc (static)] = Hc (dynamic) [Dc (dynamic)]. We compared our results with the dynamic value of Hc obtained via Monte Carlo simulation out of balance and show that there is a satisfactory agreement in quantitative terms. The energy of the system represented by the Blume-Capel model with oscillating external field does not remain fixed over of evolution, swinging every second of time, so can not obtain the static properties of the formalism of equilibrium statistical mechanics. Returned diagrams phase regions where we find ordered (ferromagnetic), disordered (paramagnetic) and regions of coexistence