Effective dynamics and steady state of an Ising model submitted to tapping processes

A. Prados; J. Javier Brey

doi:10.1103/physreve.66.041308

Home/Archive/arXiv

arXiv · cond-mat/0207049

Effective dynamics and steady state of an Ising model submitted to tapping processes

A. Prados·J. Javier Brey

View original source ↗Read source document ↗Export metadata ↓

Abstract

A one-dimensional Ising model with nearest neighbour interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the Ising model. Trying to mimic the experiments, a series of taps separated by large enough waiting times, for which the system freely relaxes, is considered. The free relaxation of the system corresponds to a T=0 dynamics which can be analytically solved. There is an extensive number of metastable states, characterized by all the holes being isolated. In the limit of weak tapping, an effective dynamics connecting the metastable states is obtained. The steady state of this dynamics is analyzed, and the probability distribution function is shown to have the canonical form. Then, the stationary state is described by Edwards thermodynamic granular theory. Spatial correlation functions in the steady state are also studied.

Explore related subjects

cond-mat.stat-mech cond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

A. Prados, J. Javier Brey. 2002-09-04. Effective dynamics and steady state of an Ising model submitted to tapping processes. https://doi.org/10.1103/physreve.66.041308

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗

arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗

arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗