Large deviations of the finite-time magnetization of the Curie-Weiss random-field Ising model

作者：Paga Pierre^*; Kuhn Reimer

来源：PHYSICAL REVIEW E, 2017, 96(2): 022126.

DOI：10.1103/PhysRevE.96.022126

We study the large deviations of the magnetization at some finite time in the Curie-Weiss random field Ising model with parallel updating. While relaxation dynamics in an infinite-time horizon gives rise to unique dynamical trajectories [specified by initial conditions and governed by first-order dynamics of the form m(t+1) = f (-1)(m(t))], we observe that the introduction of a finite-time horizon and the specification of terminal conditions can generate a host of metastable solutions obeying second-order dynamics. We show that these solutions are governed by a Newtonian-like dynamics in discrete time which permits solutions in terms of both the first-order relaxation ("forward") dynamics and the backward dynamics m(t+1) = f(-1)(m(t)). Our approach allows us to classify trajectories for a given final magnetization as stable or metastable according to the value of the rate function associated with them. We find that in analogy to the Freidlin-Wentzell description of the stochastic dynamics of escape from metastable states, the dominant trajectories may switch between the two types (forward and backward) of first-order dynamics. Additionally, we show how to compute rate functions when uncertainty in the quenched disorder is introduced.

• 出版日期2017-8-14