Related papers: Study of the disordered one-dimensional contact pr…
The equilibrium and non--equilibrium disorder induced phase transitions are compared in the random-field Ising model (RFIM). We identify in the demagnetized state (DS) the correct non-equilibrium hysteretic counterpart of the T=0 ground…
We investigate classes of interacting systems that allow for a mapping to disordered noninteracting systems. As we show, such a mapping is possible for interacting systems with a suppressed density of states at the chemical potential,…
In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
The problem of random walk is considered in one dimension in the simultaneous presence of a quenched random force field and long-range connections the probability of which decays with the distance algebraically as p_l ~ \beta l^{-s}. The…
We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder…
The Contact Process has been studied on complex networks exhibiting different kinds of quenched disorder. Numerical evidence is found for Griffiths phases and other rare region effects, in Erd\H os R\'enyi networks, leading rather…
The two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra.…
We present an extensive study of the effects of quenched disorder on the dynamic phase transitions of kinetic spin models in two dimensions. We undertake a numerical experiment performing Monte Carlo simulations of the square-lattice…
We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean field theory (DMFT) and the equilibrium coherent potential approximation (CPA)…
The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for…
One investigates the flat phase of quenched disordered polymerized membranes by means of a two-loop, weak-coupling computation performed near their upper critical dimension $D_{uc} = 4$, generalizing the one-loop computation of Morse,…
We present a new numerical approach to the study of disorder and interactions in quasi-1D systems which combines aspects of the transfer matrix method and the density matrix renormalization group which have been successfully applied to…
The disorder operator, as an easily measured non-local observable, displays great potential in detecting intrinsic information of field theories. It has been systematically studied in 1d and 2d quantum systems, while the knowledge of 3d is…
A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations…
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…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not…
We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a…
We investigate finite size scaling aspects of disorder reaction-diffusion processes in one dimension utilizing both numerical and analytical approaches. The former averages the spectrum gap of the associated evolution operators by doubling…