Avalanches and the Renormalization Group for Pinned Charge-Density Waves

The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization group treatment can be used successfully to find the divergences in the polarization and the correlation length, and, to first order in an $\epsilon = 4-d$ expansion, the diverging time scale. The automaton models studied are a charge-density wave model and a ``sandpile'' model with periodic boundary conditions; these models are found to have the same critical behavior, associated with diverging avalanche sizes. The numerical results for the polarization and the diverging length and time scales in dimensions $d=2,3$ are in agreement with the analytical treatment. These results clarify the connections between the behaviour above and below threshold: the characteristic correlation lengths on both sides of the transition diverge with different exponents. The scaling of the distribution of avalanches on the approach to threshold is found to be different for automaton and continuous-variable models.Comment: 29 pages, 11 postscript figures included, REVTEX v3.0 (dvi and PS files also available by anonymous ftp from external.nj.nec.com in directory /pub/alan/cdwfigs

Random background charges and Coulomb blockade in one-dimensional tunnel junction arrays

We have numerically studied the behavior of one dimensional tunnel junction arrays when random background charges are included using the ``orthodox'' theory of single electron tunneling. Random background charge distributions are verified in both amplitude and density. The use of a uniform array as a transistor is discussed both with and without random background charges. An analytic expression for the gain near zero gate voltage in a uniform array with no background charges is derived. The gate modulation with background charges present is simulated.Comment: 10 pages, 7 figure

The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states

The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim L^\zeta$, is consistent with the theoretical prediction $\zeta = 2/3$. As the randomness is increased through the transition, the probability distribution of the interfacial tension of domain walls scales as for a single second order transition. At the critical point, the fractal dimensions of domain walls and the fractal dimension of the outer surface of spin clusters are investigated: there are at least two distinct physically important fractal dimensions. These dimensions are argued to be related to combinations of the energy scaling exponent, $\theta$, which determines the violation of hyperscaling, the correlation length exponent $\nu$, and the magnetization exponent $\beta$. The value $\beta = 0.017\pm 0.005$ is derived from the magnetization: this estimate is supported by the study of the spin cluster size distribution at criticality. The variation of configurations in the interior of a sample with boundary conditions is consistent with the hypothesis that there is a single transition separating the disordered phase with one ground state from the ordered phase with two ground states. The array of results are shown to be consistent with a scaling picture and a geometric description of the influence of boundary conditions on the spins. The details of the algorithm used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure

Velocity-force characteristics of a driven interface in a disordered medium

Using a dynamic functional renormalization group treatment of driven elastic interfaces in a disordered medium, we investigate several aspects of the creep-type motion induced by external forces below the depinning threshold $f_c$: i) We show that in the experimentally important regime of forces slightly below $f_c$ the velocity obeys an Arrhenius-type law $v\sim\exp[-U(f)/T]$ with an effective energy barrier $U(f)\propto (f_{c}-f)$ vanishing linearly when f approaches the threshold $f_c$. ii) Thermal fluctuations soften the pinning landscape at high temperatures. Determining the corresponding velocity-force characteristics at low driving forces for internal dimensions d=1,2 (strings and interfaces) we find a particular non-Arrhenius type creep $v\sim \exp[-(f_c(T)/f)^{\mu}]$ involving the reduced threshold force $f_c(T)$ alone. For d=3 we obtain a similar v-f characteristic which is, however, non-universal and depends explicitly on the microscopic cutoff.Comment: 9 pages, RevTeX, 3 postscript figure

Creep motion in a random-field Ising model

We analyze numerically a moving interface in the random-field Ising model which is driven by a magnetic field. Without thermal fluctuations the system displays a depinning phase transition, i.e., the interface is pinned below a certain critical value of the driving field. For finite temperatures the interface moves even for driving fields below the critical value. In this so-called creep regime the dependence of the interface velocity on the temperature is expected to obey an Arrhenius law. We investigate the details of this Arrhenius behavior in two and three dimensions and compare our results with predictions obtained from renormalization group approaches.Comment: 6 pages, 11 figures, accepted for publication in Phys. Rev.

Effects of disorder on the wave front depinning transition in spatially discrete systems

Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and subject to random external forces. The presence of weak randomness shrinks the pinning interval and it changes the critical exponent of the wave front depinning transition from 1/2 to 3/2. This effect is derived by means of a recent asymptotic theory of the depinning transition, extended to discrete drift-diffusion models of transport in semiconductor superlattices and confirmed by numerical calculations.Comment: 4 pages, 3 figures, to appear as a Rapid Commun. in Phys. Rev.

Critical States in a Dissipative Sandpile Model

A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is mean-field like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behaviour of same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included

Mott insulators in strong electric fields

Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of Rb atoms. This state is stable to a small applied potential gradient (an `electric' field), but a resonant response was observed when the potential energy drop per lattice spacing (E), was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for E close to U via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order, and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions, and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions, and to a variety of lattices, should allow study of numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference

Monte Carlo Dynamics of driven Flux Lines in Disordered Media

We show that the common local Monte Carlo rules used to simulate the motion of driven flux lines in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss a class of generalized Monte Carlo algorithms where an arbitrary number of line elements may move at the same time. We prove that all these dynamical rules have the same value of the critical force and possess phase spaces made up of a single ergodic component. A variant Monte Carlo algorithm allows to compute the critical force of a sample in a single pass through the system. We establish dynamical scaling properties and obtain precise values for the critical force, which is finite even for an unbounded distribution of the disorder. Extensions to higher dimensions are outlined.Comment: 4 pages, 3 figure

Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines

The dynamical critical behavior of a single directed line driven in a random medium near the depinning threshold is studied both analytically (by renormalization group) and numerically, in the context of a Flux Line in a Type-II superconductor with a bulk current $\vec J$. In the absence of transverse fluctuations, the system reduces to recently studied models of interface depinning. In most cases, the presence of transverse fluctuations are found not to influence the critical exponents that describe longitudinal correlations. For a manifold with $d=4-\epsilon$ internal dimensions, longitudinal fluctuations in an isotropic medium are described by a roughness exponent $\zeta_\parallel=\epsilon/3$ to all orders in $\epsilon$, and a dynamical exponent $z_\parallel=2-2\epsilon/9+O(\epsilon^2)$. Transverse fluctuations have a distinct and smaller roughness exponent $\zeta_\perp=\zeta_\parallel-d/2$ for an isotropic medium. Furthermore, their relaxation is much slower, characterized by a dynamical exponent $z_\perp=z_\parallel+1/\nu$, where $\nu=1/(2-\zeta_\parallel)$ is the correlation length exponent. The predicted exponents agree well with numerical results for a flux line in three dimensions. As in the case of interface depinning models, anisotropy leads to additional universality classes. A nonzero Hall angle, which has no analogue in the interface models, also affects the critical behavior.Comment: 26 pages, 8 Postscript figures packed together with RevTeX 3.0 manuscript using uufiles, uses multicol.sty and epsf.sty, e-mail [email protected] in case of problem