Weakly disordered absorbing-state phase transitions

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.Comment: 4 pages, 2 eps figures; (v2) references and discussion on experiments added; (v3) published version, minor typos corrected, some side discussions dropped due to size constrain

One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder

Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one dimensional, non-equilibrium kinetic Ising models with locally broken spin symmetry, at zero temperature (the symmetry is broken through spin-flip rates that differ for '+' and '-' spins). The model is found to exhibit a continuous phase transition to an absorbing state. The associated critical behavior is studied at zero branching rate of kinks, through analysis spreading of '+' and '-' spins and, of the kink density. Impurities exert a strong effect on the critical behavior only for a particular choice of parameters, corresponding to the strongly spin-anisotropic kinetic Ising model introduced by Majumdar et al. Typically, disorder effects become evident for impurity strengths such that diffusion is nearly blocked. In this regime, the critical behavior is similar to that arising, for example, in the one-dimensional diluted contact process, with Griffiths-like behavior for the kink density. We find variable cluster exponents, which obey a hyperscaling relation, and are similar to those reported by Cafiero et al. We also show that the isotropic two-component AB -> 0 model is insensitive to reaction-disorder, and that only logarithmic corrections arise, induced by strong disorder in the diffusion rate.Comment: 10 pages, 13 figures. Final, accepted form in PRE, including a new table summarizing the molde

Critical behavior and Griffiths effects in the disordered contact process

We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte-Carlo simulations for times up to $10^9$ and system sizes up to $10^7$ sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of $10^4$ or larger. In the Griffiths region between the clean and the dirty critical points, we find power-law dynamical behavior with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder.Comment: 10 pages, 8 eps figures, final version as publishe

First Passage Time in a Two-Layer System

As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function formalism and a variety of analytic and numerical techniques, we calculate the asymptotic behavior of the first passage time probability distribution. We show analytically that the asymptotic distribution is a simple exponential in time for any choice of the velocities. The decay constant is given in terms of the largest eigenvalue of an operator related to a half-space Green's function. For the anti-symmetric case of opposite velocities in the layers, we show that the decay constant for system length $L$ crosses over from $L^{-2}$ behavior in diffusive limit to $L^{-1}$ behavior in the convective regime, where the crossover length $L^*$ is given in terms of the velocities. We also have formulated a general self-consistency relation, from which we have developed a recursive approach which is useful for studying the short time behavior.Comment: LaTeX, 28 pages, 7 figures not include

Strong disorder fixed point in absorbing state phase transitions

The effect of quenched disorder on non-equilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behaviour is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: \beta=(3-\sqrt{5})/2 and \nu_\perp=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.Comment: final version as accepted for PRL, contains new results in two dimension

Generalized contact process on random environments

Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent background, this transition is equivalent to those found in homogeneous systems (i.e. to directed percolation). For frozen backgrounds, the appearance of Griffiths phase prevents the accurate analysis of this transition. For long times in the subcritical region, spreading remains localized in compact (rather than ramified) patches, and the average number of occupied sites increases logarithmically in the surviving trials.Comment: 6 pages, 7 figure

Sliding blocks with random friction and absorbing random walks

With the purpose of explaining recent experimental findings, we study the distribution $A(\lambda)$ of distances $\lambda$ traversed by a block that slides on an inclined plane and stops due to friction. A simple model in which the friction coefficient $\mu$ is a random function of position is considered. The problem of finding $A(\lambda)$ is equivalent to a First-Passage-Time problem for a one-dimensional random walk with nonzero drift, whose exact solution is well-known. From the exact solution of this problem we conclude that: a) for inclination angles $\theta$ less than \theta_c=\tan(\av{\mu}) the average traversed distance \av{\lambda} is finite, and diverges when $\theta \to \theta_c^{-}$ as \av{\lambda} \sim (\theta_c-\theta)^{-1}; b) at the critical angle a power-law distribution of slidings is obtained: $A(\lambda) \sim \lambda^{-3/2}$. Our analytical results are confirmed by numerical simulation, and are in partial agreement with the reported experimental results. We discuss the possible reasons for the remaining discrepancies.Comment: 8 pages, 8 figures, submitted to Phys. Rev.

Instability of metal-insulator transition against thermal cycling in phase separated Cr-doped manganites

We show that metal-insulator transition in Pr0.5Ca0.5Mn1-xCrxO3 (x = 0.015-0.025) is unstable against thermal cycling. Insulator-metal transition shifts down and low temperature resistivity increases each time when the sample is cycled between a starting temperature TS and a final temperature TF. The effect is dramatic lower is x. Insulator-metal transition in x = 0.015 can be completely destroyed by thermal cycling in absence of magnetic field as well as under H = 2 T. Magnetic measurements suggest that ferromagnetic phase fraction decreases with thermal cycling. We suggest that increase in strains in ferromagnetic- charge ordered interface could be a possible origin of the observed effect.Comment: 14 pages, 5 figures and 2 tables (revised

Diffusion and Trapping on a one-dimensional lattice

The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of disorder and traps yields a decreasing survival probability with broad distribution (log-normal). Exact enumerations, effective-medium approximation and spectral analysis are employed. This one-dimensional model shows rather rich behaviours which were previously believed to exist only in higher dimensionality. The possibility of a trapping-dominated super universal class is suggested.Comment: 20 pages, Revtex 3.0, 13 figures in compressed format using uufiles command, to appear in Phys. Rev. E, for an hard copy or problems e-mail to: [email protected]

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states