Noise effects in a finite-size Ising-like model

Abstract

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 (±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.

2D spin-crossover hexagonal molecular nanoparticles

“…[19][20][21][22][23] As one of the simplest examples, an infinite-range Ising model under Glauber dynamics has previously been studied. 24 For our study because of the HS and LS states have different energies and degeneracies we use the phenomenological microscopic Ising-like model for describing the behavior of spin-crossover regular crystals at molecular level. In this case the intermolecular interaction is considered with the following Hamiltonian for a lattice of N spin-active centers, each interacting with z neighbors:…”

Analysis of the finite-size effect of the long-range Ising model under Glauber dynamics

“…As one of the simplest examples, an infinite-range Ising model under Glauber dynamics has previously been studied [17][18][19][20]. Most of these studies considered the probability density function of magnetization, P whole (m), and derived the Fokker-Planck equation to describe the time development of this function.…”

Analysis of finite-size effect of infinite-range Ising model under Glauber dynamics

“…However, its consideration in nonequilibrium systems is generally more difficult than in equilibrium ones. Hence, an infinite-range Ising model under the Glauber dynamics, one of the simplest models of such systems, has been studied as an example [1,2,3,4]. Most of these studies considered the probability density function of magnetization, P whole (m ′ ), and used the Fokker-Planck equation describing the time development of this function.…”