Mesoscopic description of the annealed Ising model and Multiplicative noise
Abstract
A new type of Langevin equation exhibiting a non trivial phase transition associated with the presence of multiplicative noise is introduced. The equation is derived as a mesoscopic representation of the microscopic annealed Ising model (AIM) proposed by Thorpe and Beeman, and reproduces perfectly its basic phenomenology. The AIM exhibits a non-trivial behavior as the temperature is increased, in particular it presents a disorder-to-order phase transition at low temperatures, and a order-to-disorder transition at higher temperatures. This behavior resembles that of some Langevin equations with multiplicative noise, which exhibit also two analogous phase transitions as the noise-amplitude is increased. By comparing the standard models for noise-induced transitions with our new Langevin equation we elucidate that the mechanisms controlling the disorder-to-order transitions in both of them are essentially different, even though for both of them the presence of multiplicative noise is a key ingredient.
Keywords
Cite
@article{arxiv.cond-mat/9807157,
title = {Mesoscopic description of the annealed Ising model and Multiplicative noise},
author = {Walter Genovese and Miguel A. Muñoz and P. L. Garrido},
journal= {arXiv preprint arXiv:cond-mat/9807157},
year = {2016}
}
Comments
Submitted to Phys. Rev. E