We study finite-size effects on properties of stationary state and also transient process of a bistable system with long range interaction. We adopt an Ising-like model with infinite range interaction (Husimi-Temperlay model). In particular, we formulate this problem in light of the Langevin equation and investigate study the effects of various types of noises. We study characteristics of the probability of stationary state of a finite system and find that there exist two types of regions in the ordered state: the saturated region in which the maximum of the distribution locates at the maximum value of the Ising variable ($\pm 1$) and the transient region in which the maximum of the distribution locates at a nonsaturated value. We introduce an additional type of noise that represents fluctuation due to direct coupling to the thermal bath. Finally we also study the finite-size effects on the dynamical aspect by studying the mean first-passage times.

• Received 19 May 2011

DOI:https://doi.org/10.1103/PhysRevE.84.031126