Understanding scale invariance in a minimal model of complex relaxation phenomena

Hurtado, Pablo I.; Marro, Joaquín; Garrido, P. L.

doi:10.1088/1742-5468/2006/02/p02004

Cited by 3 publications

(2 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…( 28) and appendix B-and (large) avalanches is also supported by experiments (35; 36; 37). On the other hand, it is remarkable that the statistical properties of the resulting distributions are indistinguishable in practice from actual data (38). For instance, size corrections similar to the ones in eqs.…”

Section: Some Additional Commentsmentioning

confidence: 96%

Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder

2008

View full text Add to dashboard Cite

We study both analytically and numerically demagnetization via nucleation of the metastable phase in a two-dimensional nonequilibrium Ising ferromagnet at temperature T . Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of undetermined source. We present a simple theoretical description, in perfect agreement with Monte Carlo simulations, assuming that the decay of the nonequilibrium metastable state is due, as in equilibrium, to the competition between the surface and the bulk. This suggests one to accept a nonequilibrium free-energy at a mesoscopic/cluster level, and it ensues a nonequilibrium surface tension with some peculiar low-T behavior. We illustrate the occurrence of intriguing nonequilibrium phenomena, including: (i) stochastic resonance phenomena at low T which stabilize the metastable state as temperature increases; (ii) reentrance of the limit of metastability under strong nonequilibrium conditions; and (iii) noise-enhanced propagation of domain walls. The cooperative behavior of our system, which is associated to the interplay between thermal and nonequilibrium fluctuations, may also be understood in terms of a Langevin equation with additive and multiplicative noises. We also studied metastability in the case of open boundaries as it may correspond to a magnetic nanoparticle. We then observe the most irregular relaxation triggered by the additional surface randomness. In particular, at low T, the relaxation becomes discontinuous as occurring by way of scale-free avalanches, so that it resembles the type of relaxation reported for many complex systems. We show that this results from the superposition of many demagnetization events, each with a well-defined scale which is determined by the curvature of the domain wall at which it originates. This is an example of (apparent) scale invariance in a nonequilibrium setting which is not to be associated with any familiar kind of criticality. a metastable state in a properly constrained (equilibrium) ensemble (2; 3; 9), and that most equilibrium concepts may easily be adapted (4; 5; 6; 7; 8).In this paper we present a detailed study of metastability (and nucleation) in a nonequilibrium model. In order to deal with a simple microscopic model of metastability, we study a two-dimensional kinetic Ising system, as in previous studies. However, for the system to exhibit nonequilibrium behavior, time evolution is defined here as a superposition of the familiar thermal process at temperature T and a weak completely-random process. This competition is probably one of the simplest, both conceptually and operationally, ways of impeding equilibrium. Furthermore, one may argue that it captures some underlying disorder induced by random impurities or other causes which are unavoidable in actual samples. The specific origin for such dynamic randomness will vary with the situation considered. We mention that a similar mechanism has already been used to model the macroscopic consequences of rapidly-diffusing local ...

show abstract

Section: Some Additional Commentsmentioning

confidence: 96%

Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder

2008

View full text Add to dashboard Cite

show abstract

“…However, similar dynamic impurities play a fundamental role in some natural systems. As a matter of fact, an equivalent mechanism has been used to model the macroscopic consequences of rapidly-diffusing local defects [10] and quantum tunneling [11] in magnetic samples and, more generally, the origin of scale-invariant avalanches [14].…”

mentioning

confidence: 99%

Metastability, nucleation, and noise-enhanced stabilization out of equilibrium

2006

View full text Add to dashboard Cite

We study metastability and nucleation in a kinetic two-dimensional Ising model that is driven out of equilibrium by a small random perturbation of the usual dynamics at temperature T. We show that, at a mesoscopic/cluster level, a nonequilibrium potential describes in a simple way metastable states and their decay. We thus predict noise-enhanced stability of the metastable phase and resonant propagation of domain walls at low T. This follows from the nonlinear interplay between thermal and nonequilibrium fluctuations, which induces reentrant behavior of the surface tension as a function of T. Our results, which are confirmed by Monte Carlo simulations, can be also understood in terms of a Langevin equation with competing additive and multiplicative noises.

show abstract