Quenched and annealed disorder mechanisms in comb models with fractional operators (original) (raw)

Absorbing state phase transitions with quenched disorder

Physical Review E, 2004

Quenched disorder-in the sense of the Harris criterion-is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for a weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis. PACS number(s): 05.70.Ln, 05.70.Jk, 64.60.Ak

Disorder-driven transition in a chain with power-law hopping

Physical Review B, 2015

We study a 1D system with a power-law quasiparticle dispersion ∝ |k| α sgn k in the presence of a short-range-correlated random potential and demonstrate that for α < 1/2 it exhibits a disorderdriven quantum phase transition with the critical properties similar to those of the localisation transition near the edge of the band of a semiconductor in high dimensions, studied in Refs. [1] and [2]. Despite the absence of localisation in the considered 1D system, the disorder-driven transition manifests itself, for example, in a critical form of the disorder-averaged density of states. We confirm the existence of the transition by numerical simulations and find the critical exponents and the critical disorder strength as a function of α. The proposed system thus presents a convenient platform for numerical studies of the recently predicted unconventional high-dimensional localisation effects and has the potential for experimental realisations in chains of ultracold atoms in optical traps.

Quenched disorder: Demixing thermal and disorder fluctuations

Physical Review E, 2012

We present a finite size scaling study of the phase transition in the 2d Potts model modified by random bond disorder, in which the average is taken over quantities calculated at quasicritical temperatures of individual disorder configurations. We used the recently proposed Equilibriumlike invaded cluster algorithm, which allows to examine separately the fluctuations in the thermodynamical ensemble from the fluctuations induced by changing the disorder configuration. We point out the crucial role of the spatial inhomogeneities on all scales for the critical behavior of the system. These inhomogeneities are formed by "dressing" of the disorder via critical correlations and are demonstrated to exist for any system size despite of the critical fluctuations in thermodynamical ensemble. Such inhomogeneities were previously not thought to be relevant in disorder altered classical systems when critical temperature is finite. However, we confirm that only by averaging at quasicritical temperatures of each disorder configuration, the thermal critical exponent y τ is not obscured by the influence of the aforementioned spatial inhomogeneities.

Fractional exclusion statistics in disordered interacting systems

arXiv (Cornell University), 2012

We develop a model based on the fractional exclusion statistics (FES) applicable to non-homogeneous interacting particle systems. Here the species represent elementary volumes in an (s+1)-dimensional space, formed by the direct product between the s-dimensional space of positions and the quasiparticle energy axis. The model is particularly suitable for systems with localized states. We prove the feasibility of our method by applying it to systems of different degrees of complexities. We first apply the formalism on simpler systems, formed of two sub-systems, and present numerical and analytical thermodynamic calculations, pointing out the quasiparticle population inversion and maxima in the heat capacity, in contrast to systems with only diagonal (direct) FES parameters. Further we investigate larger, non-homogeneous systems with repulsive screened Coulomb interactions, indicating accumulation and depletion effects at the interfaces. Finally, we consider systems with several degrees of disorder, which are prototypical for models with glassy behavior. We find that the disorder produces a spatial segregation of quasiparticles at low energies which significantly affects the heat capacity and the entropy of the system.

Extended states in disordered systems: Role of off-diagonal correlations

Physical Review B, 2004

We study one-dimensional systems with random diagonal disorder but off-diagonal short-range correlations imposed by structural constraints. We find that these correlations generate effective conduction channels for finite systems. At a certain golden correlation condition for the hopping amplitudes, we find an extended state for an infinite system. Our model has important implications to charge transport in DNA molecules, and a possible set of experiments in semiconductor superlattices is proposed to verify our most interesting theoretical predictions.

Coarsening and percolation in the Ising Model with quenched disorder

Journal of Physics: Conference Series, 2018

Through large-scale numerical simulations, we study the phase ordering kinetics of the 2d Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities-the winding angle and the pair-connectedness-we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model.

Distribution of spectral-flow gaps in the Rashba model with disorder: a new universality

2006

We report a study of disordered electron systems with spin-orbit coupling on a cylinder using methods of random matrix ensembles. With a threading flux turned on, the single particle levels will generally avoid, rather than cross, each other. Our numerical study of the level-avoiding gaps in the disordered Rashba model demonstrates that the normalized gap distribution is of a universal form, independent of the random strength and the system size. For small gaps it exhibits a linear behavior, while for large gaps it decays exponentially. A framework based on matrix mechanical models is suggested, and is verified to reproduce the universal linear behavior at small gaps. Thus we propose to use the distribution of the spectral-flow gaps associated with flux insertion as a new way to characterize 2d random systems with spin-orbit coupling. The relevance and qualitative implications for spin (Hall) transport are also addressed.