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We study numerically the phase-ordering kinetics of the site-diluted and bond-diluted Ising models after a quench from an infinite to a low temperature. We show that the speed of growth of the ordered domains size is non-monotonous with respect to the amount of dilution $D$: Starting from the pure case $D=0$ the system slows down when dilution is added, as it is usually expected when disorder is introduced, but only up to a certain value $D^*$ beyond which the speed of growth raises again. We interpret this counterintuitive fact in a renormalization-group inspired framework, along the same lines proposed for the corresponding two-dimensional systems, where a similar pattern was observed.
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We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth-laws of the ordered domains size - logarithmic or power-law respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature which governs the presence or the absence of a finite-temperature phase-transition.
We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent $a_chi$ for the integrated response function, at variance with all the other exponents, is independent on temperature and on the presence of pinning. This universal character suggests a strict relation between $a_chi$ and the topological properties of the networks, in analogy to what observed on regular lattices.
The effects of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class are revisited. Using a strong-disorder energy-space renormalization group, it is shown that for any amount of disorder the critical behavior is controlled by an infinite-randomness fixed point in the universality class of the random transverse-field Ising models. The experimental relevance of our results are discussed.
In a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits super-diffusion. In the context of glass forming systems, super cooled glasses and contamination spreading in porous medium it was suggested to model this behavior with a biased continuous time random walk. Here we analyze the plume of particles far lagging behind the mean, with the single big jump principle. Revealing the mechanism of the anomaly, we show how a single trapping time, the largest one, is responsible for the rare fluctuations in the system. These non typical fluctuations still control the behavior of the mean square displacement, which is the most basic quantifier of the dynamics in many experimental setups. We show how the initial conditions, describing either stationary state or non-equilibrium case, persist for ever in the sense that the rare fluctuations are sensitive to the initial preparation. To describe the fluctuations of the largest trapping time, we modify Fr{e}chets law from extreme value statistics, taking into consideration the fact that the large fluctuations are very different from those observed for independent and identically distributed random variables.
We consider two models with disorder dominated critical points and study the distribution of clusters which are confined in strips and touch one or both boundaries. For the classical random bond Potts model in the large-q limit we study optimal Fortuin-Kasteleyn clusters by combinatorial optimization algorithm. For the random transverse-field Ising chain clusters are defined and calculated through the strong disorder renormalization group method. The numerically calculated density profiles close to the boundaries are shown to follow scaling predictions. For the random bond Potts model we have obtained accurate numerical estimates for the critical exponents and demonstrated that the density profiles are well described by conformal formulae.
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