Critical behavior and out-of-equilibrium dynamics of a two-dimensional Ising model with dynamic couplings

We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest neighbors of each spin pair, which prevents the system from ordering in a full ferromagnetic or antiferromagnetic state. Using a parallel-tempering Monte Carlo algorithm, we find that the model undergoes a continuous phase transition at finite temperature, which belongs to the Ising universality class. The properties of the bond structure and the ground-state entropy are also studied. Finally, we analyze the out-of-equilibrium dynamics which displays typical glassy characteristics at a temperature well below the critical one.Comment: 10 pages with 12 figure

Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium

We numerically study the geometry of a driven elastic string at its sample-dependent depinning threshold in random-periodic media. We find that the anisotropic finite-size scaling of the average square width $\bar{w^2}$ and of its associated probability distribution are both controlled by the ratio $k=M/L^{\zeta_{\mathrm{dep}}}$, where $\zeta_{\mathrm{dep}}$ is the random-manifold depinning roughness exponent, $L$ is the longitudinal size of the string and $M$ the transverse periodicity of the random medium. The rescaled average square width $\bar{w^2}/L^{2\zeta_{\mathrm{dep}}}$ displays a non-trivial single minimum for a finite value of $k$. We show that the initial decrease for small $k$ reflects the crossover at $k \sim 1$ from the random-periodic to the random-manifold roughness. The increase for very large $k$ implies that the increasingly rare critical configurations, accompanying the crossover to Gumbel critical-force statistics, display anomalous roughness properties: a transverse-periodicity scaling in spite that $\bar{w^2} \ll M$, and subleading corrections to the standard random-manifold longitudinal-size scaling. Our results are relevant to understanding the dimensional crossover from interface to particle depinning.Comment: 11 pages, 7 figures, Commentary from the reviewer available in Papers in Physic

Non-steady relaxation and critical exponents at the depinning transition

We study the non-steady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units (GPUs). We compute the time-dependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, non-universal microscopic time-regime, we find a non-trivial long crossover towards the non-steady macroscopic critical regime. This "mesoscopic" time-regime is robust under changes of the microscopic disorder including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L~2^{25}) simulations for the non-steady dynamics of the continuum displacement quenched Edwards Wilkinson equation, getting accurate and consistent depinning exponents for this class: \beta = 0.245 \pm 0.006, z = 1.433 \pm 0.007, \zeta=1.250 \pm 0.005 and \nu=1.333 \pm 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent \beta) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.Comment: Published version (including erratum). Codes and Supplemental Material available at https://bitbucket.org/ezeferrero/qe

Nonequilibrium dynamics of the three-dimensional Edwards-Anderson spin-glass model with Gaussian couplings: Strong heterogeneities and the backbone picture

We numerically study the three-dimensional Edwards-Anderson model with Gaussian couplings, focusing on the heterogeneities arising in its nonequilibrium dynamics. Results are analyzed in terms of the backbone picture, which links strong dynamical heterogeneities to spatial heterogeneities emerging from the correlation of local rigidity of the bond network. Different two-times quantities as the flipping time distribution and the correlation and response functions, are evaluated over the full system and over high- and low-rigidity regions. We find that the nonequilibrium dynamics of the model is highly correlated to spatial heterogeneities. Also, we observe a similar physical behavior to that previously found in the Edwards-Anderson model with a bimodal (discrete) bond distribution. Namely, the backbone behaves as the main structure that supports the spin-glass phase, within which a sort of domain-growth process develops, while the complement remains in a paramagnetic phase, even below the critical temperature

Kinetic roughening, global quantities, and fluctuation-dissipation relations

Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but that is also directly conjugate to an experimentally accessible parameter, thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions. Exploiting the full analyticity of the linear Edwards-Wilkinson and Mullins-Herring equations, we study in detail various two-time functions related to that quantity. This quantity fulfills the fluctuation-dissipation theorem when considering steady-state equilibrium fluctuations.Comment: 13 pages, 5 figure

Random-Manifold to Random-Periodic Depinning of an Elastic Interface

We study numerically the depinning transition of driven elastic interfaces in a random-periodic medium with localized periodic-correlation peaks in the direction of motion. The analysis of the moving interface geometry reveals the existence of several characteristic lengths separating different length-scale regimes of roughness. We determine the scaling behavior of these lengths as a function of the velocity, temperature, driving force, and transverse periodicity. A dynamical roughness diagram is thus obtained which contains, at small length scales, the critical and fast-flow regimes typical of the random-manifold (or domain wall) depinning, and at large length-scales, the critical and fast-flow regimes typical of the random-periodic (or charge-density wave) depinning. From the study of the equilibrium geometry we are also able to infer the roughness diagram in the creep regime, extending the depinning roughness diagram below threshold. Our results are relevant for understanding the geometry at depinning of arrays of elastically coupled thin manifolds in a disordered medium such as driven particle chains or vortex-line planar arrays. They also allow to properly control the effect of transverse periodic boundary conditions in large-scale simulations of driven disordered interfaces.Comment: 19 pages, 10 figure