Narrow Results

The scaling properties of interfaces generated by a disaggregation model in 1+1 dimensions are studied by numerical simulations. The model presented here for the disaggregation process takes into account the possibility of having quenched disorder in the bulk under deconstruction. The disorder can be considered to model several types of irregularities appearing in real materials (dislocations, impurities). The presence of irregularities makes the intensity of the attack to be not uniform. In order to include this effect, the computational bulk is considered to be composed by two types of particles: those particles which can be easily detached and other particles that are not sensible to the etching attack. As the detachment of particles proceeds in time, the dynamical properties of the rough interface are studied. The resulting one-dimensional surface show self-affine properties and the values of the scaling exponents are reported when the interface is still moving near the depinning transition. According to the scaling exponents presented here, the model must be considered to belong to a new universality class.

Front propagation in a random environment is studied close to the depinning threshold. At zero temperature we show that the depinning force distribution exhibits a universal behavior. This property is used to estimate the velocity of the front at very low temperature. We obtain a Arrhenius behavior with a prefactor depending on the temperature as a power law. These results are supported by numerical simulations.

In this review paper, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of the available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range correlated random-site disorder, and (iii) random anisotropy.

Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of this review is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.

In this paper, we present a theory of phase transition in quantum critical paraelectrics in presence of quenched random-T_c disorder using replica trick. The effects of disorder induced locally ordered regions and their slow dynamics are included by breaking the replica symmetry at vector level. The occurrence of a mixed phase at any finite value of disorder strength is argued. A broad power law distribution of quantum critical points and and its finite temperature consequences are predicted. Results are interesting in the context of a certain class of disordered materials near quantum phase transition.

A Hartree–Fock mean-field theory of a weakly interacting Bose-gas in a quenched white noise disorder potential is presented. A direct continuous transition from the normal gas to a localized Bose-glass phase is found which has localized short-lived excitations with a gapless density of states and vanishing superfluid density. The critical temperature of this transition is as for an ideal gas undergoing Bose–Einstein condensation. Increasing the particle-number density a first-order transition from the localized state to a superfluid phase perturbed by disorder is found. At intermediate number densities both phases can coexist.

We analyze the impact of a porous medium (structural disorder) on the scaling of the partition function of a star polymer immersed in a good solvent. We show that corresponding scaling exponents change if the disorder is long-range-correlated and calculate the exponents in the new universality class. A notable finding is that star and chain polymers react in qualitatively different manner on the presence of disorder: the corresponding scaling exponents increase for chains and decrease for stars. We discuss the physical consequences of this difference.

The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results bring about the estimates of critical exponents, governing the scaling laws of disorder averages of the configurational properties of SAWs.