Field-Tuned Superconductor-Insulator Transition with and without Current Bias

The magnetic-field-tuned superconductor-insulator transition has been studied in ultrathin beryllium films quench condensed near 20 K. In the zero-current limit, a finite-size scaling analysis yields the scaling exponent product nuz = 1.35+/-0.10 and a critical sheet resistance, R(c), of about 1.2R(Q), with R(Q) = h/4e(2). However, in the presence of dc bias currents that are smaller than the zero-field critical currents, nuz becomes 0.75+/-0.10. This new set of exponents suggests that the field-tuned transitions with and without a dc bias current belong to different universality classes.     

Nagel scaling, relaxation, and universality in the kinetic ising model on an alternating isotopic chain

The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model on an alternating isotopic chain with Glauber dynamics are examined. The analysis provides a connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may exhibit plateau regions and does not hold for all temperatures.     

Critical dynamics of the dirty boson problem: revisiting the equality z=d

It is shown that previous arguments, leading to the equality z=d for the dynamical exponent describing the Bose glass to superfluid transition in d dimensions, may break down, as apparently seen in recent simulations. The key observation is that the major contribution to the compressibility, which remains finite through the transition and was predicted to scale as kappa approximately |delta|((d-z)nu) (where delta is the deviation from criticality and nu is the correlation length exponent) comes from the analytic, not the singular part of the free energy, and is not restricted by any conventional scaling hypothesis.     

Nonlinear electric field effects at a continuous mott-hubbard transition

We characterize the non-Ohmic portion of the conductivity at temperatures T<1 K in the highly correlated transition metal chalcogenide Ni(S,Se)(2). Pressure tuning of the T = 0 metal-insulator transition reveals the influence of the quantum critical point and permits a direct determination of the dynamical critical exponent z = 2.7(+0.3)(-0.4). Within the framework of finite temperature scaling, we find that the spatial correlation length exponent nu and the conductivity exponent &mgr; differ.     

Length-scale-dependent relaxation in colloidal gels

We use molecular dynamics computer simulations to investigate the relaxation dynamics of a simple model for a colloidal gel at a low volume fraction. We find that due to the presence of the open spanning network this dynamics shows at low temperature a nontrivial dependence on the wave vector which is very different from the one observed in dense glass-forming liquids. At high wave vectors the relaxation is due to the fast cooperative motion of the branches of the gel network, whereas at low wave vectors the overall rearrangements of the heterogeneous structure produce the relaxation process.     

Freezing of dynamical exponents in low dimensional random media

A particle in a random potential with logarithmic correlations in dimensions d = 1,2 is shown to undergo a dynamical transition at T(dyn)>0. In d = 1 exact results show T(dyn) = T(c), the static glass transition temperature, and that the dynamical exponent changes from z(T) = 2+2(T(c)/T)(2) at high T to z(T) = 4T(c)/T in the glass phase. The same formulas are argued to hold in d = 2. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In d = 1 a mapping between dynamics and statics is unveiled and freezing involves barriers as well as valleys. Anomalous scaling occurs in the creep dynamics, relevant to dislocation motion experiments.     

Damage-spreading dynamic scaling for the ising model on the sierpinski gasket fractal

We study the relaxation towards equilibrium of the ferromagnetic Ising model on the Sierpinski gasket, which is a fractal lattice. We do this by performing Monte Carlo simulations, based on the heat-bath dynamics, and investigating the time evolution of the Hamming distance between two different configurations of the model. Starting with an initial damage created in all lattice sites, we calculate the average values of two quantities that characterize the relaxation process: the nonlinear damage relaxation time (tau), and the time for all sites to be undamaged at least once (tau(c)). We find that tau diverges, at low temperatures, with a dynamical exponent z which depends linearly on the inverse of temperature, as predicted by a generalized scaling theory developed by Henley. There is a complete breakdown of scaling for tau(c).     

Random walks on a ( 2+1)-dimensional deformable medium

A model of random walks on a deformable medium is proposed in 2+1 dimensions. The behavior of the walk is characterized by the stability parameter beta and the stiffness exponent alpha. The average square end-to-end distance l approximately equals (2nu) and the average number of visited sites approximately equals (k) are calculated. As beta increases, for each alpha there exists a critical transition point beta(c) from purely random walks ( nu = 1/2 and k approximate to 1) to compact growth ( nu = 1/3 and k = 2/3). The relationship between beta(c) and alpha can be expressed as beta(c) = e(alpha). The landscape generated by a walk is also investigated by means of the visit-number distribution N(n)(beta). There exists a scaling relationship of the form N(n)(beta)approximately n(-2)f(n/beta(z)).     

Exotic versus conventional scaling and universality in a disordered bilayer quantum heisenberg antiferromagnet

We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.     

What do we learn from the local geometry of glass-forming liquids?

We examine the local geometry of a simulated glass-forming polymer melt. Using the Voronoi construction, we find that the distributions of Voronoi volume P(v(V)) and asphericity P(a) appear to be universal properties of dense liquids, supporting the use of packing approaches to understand liquid properties. We also calculate the average free volume along a path of constant density and find that extrapolates to zero at the same temperature T0 that the extrapolated relaxation time diverges. We relate to the Debye-Waller factor, which is measurable by neutron scattering.     

Complete condensation in a zero range process on scale-free networks

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the rate p(n) = n(delta) at which particles hop out of nodes with n particles. We show analytically that a complete condensation occurs when delta < or = delta(c) triple bond 1/(gamma-1) where gamma is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a threshold are occupied by macroscopic numbers of particles, while the other nodes are occupied by negligible numbers of particles. We also show numerically that the relaxation time follows a power-law scaling tau approximately L(z) with the network size L and a dynamic exponent z in the condensed phase.     

Critical behavior of frustrated Josephson junction arrays with bond disorder

The scaling behavior of the current-voltage (IV) characteristics of a two-dimensional proximity-coupled Josephson junction array (JJA) with quenched bond disorder was investigated for frustrations f = 1/5, 1/3, 2/5, and 1/2. For all these frustrations including 1/5 and 2/5 where a strongly first-order phase transition is expected in the absence of disorder, the IV characteristics exhibited a good scaling behavior. The critical exponent nu indicates that bond disorder may drive the phase transitions to be continuous but not into the Ising universality class, contrary to what was observed in Monte Carlo simulations. The dynamic critical exponent z for JJA's was found to be only 0.60-0.77.     

Universally diverging Grüneisen parameter and the magnetocaloric effect close to quantum critical points

At a generic quantum critical point, the thermal expansion alpha is more singular than the specific heat c(p). Consequently, the "Grüneisen ratio," Gamma=alpha/c(p), diverges. When scaling applies, Gamma approximately T(-1/(nu z)) at the critical pressure p=p(c), providing a means to measure the scaling dimension of the most relevant operator that pressure couples to; in the alternative limit T-->0 and p not equal p(c), Gamma approximately 1/(p-p(c)) with a prefactor that is, up to the molar volume, a simple universal combination of critical exponents. For a magnetic-field driven transition, similar relations hold for the magnetocaloric effect (1/T) partial differential T/ partial differential H|(S). Finally, we determine the corrections to scaling in a class of metallic quantum critical points.     

Glassy dynamics

We review dynamic processes in supercooled liquids and glasses as studied by dielectric spectroscopy. It is the only experimental technique which allows one to follow the tremendous slow-down of diffusive motion of particles in disordered condensed matter over more than 18 decades in frequency or time. The dielectric techniques used are treated in detail. As an introduction for non-specialists, the time and temperature evolution of the basic spectral features associated with various dynamic relaxation processes are discussed in detail. Among them are the structural relaxation, the occurrence of fast processes and the boson peak. The relevance of these features for glass formation is discussed. The present article may also serve as a review for recent experimental and theoretical studies on glass-forming liquids.     

Asymmetric metal-insulator transition in disordered ferromagnetic films

We present experimental data and a theoretical interpretation of the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness b ≈ 2-10 nm. A large phase relaxation rate caused by scattering of quasiparticles off spin-wave excitations renders the dephasing length L(?) ? b in the range of sheet resistances considered, so that the effective dimension is d = 3. The conductivity data at different stages of disorder obey a fractional power-law temperature dependence and collapse onto two scaling curves for the metallic and insulating regimes, indicating an asymmetric metal-insulator transition with two distinctly different critical exponents; the best fit is obtained for a dynamical exponent z ≈ 2.5 and a correlation (localization) length critical exponent ν- ≈ 1.4 (ν+ ≈ 0.8) on the metallic (insulating) side.     

GENERALIZED SCALING LAWS IN THRESHOLD PKENOMENA OF NON-EQUILIBRIUM SYSTEMS

A general discussion on threshold phenomena, namely exponent behaviors of abrupt transitions between steady states near a threshold for a non-equilibrium system satisfying potential condition and having the arbitrary values of z and c, both characteristic parameters of the system, is given. It is shown that the scaling hypothesis in general homogeneous function form holds for threshold phenomena. The expressions of the threshold exponents,β,δ,γ^′ and α^′of the threshold amplitudes, B, D, Γ^′ and A^′,and the generalized scaling laws obeyed by them are all obtained. These Iaws reduce to the same as the scaling laws in critical phenomena when z=c=1.The results support, in respect of exponent behaviors of transitions, the statement on the great similarity between the phase transitions in equilibrium systems and the abrupt transitions of steady states in non-equilibrium systems.     

Crossover from attractive to repulsive Casimir forces and vice versa

Systems described by an O(n) symmetrical varphi;{4} Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes B_{j}, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions partial differential_{n}phi=c[over composite function]_{j}phi. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} when d<4, where c_{i} are scaling fields associated with the variables c[over composite function]_{i} and Phi is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c_{1},c_{2}) at d=4- dimensions are presented. These show that (i) the Casimir force can have either sign, depending on c_{1} and c_{2}, and (ii) for appropriate choices of the enhancements c[over composite function]_{j}, crossovers from attraction to repulsion and vice versa occur as L increases.     

Fractal dimension and localization of DNA knots

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak binding, that permits (partial) relaxation on the surface. In (i) the radius of gyration of the adsorbed DNA knot scales with the 3D Flory exponent nu approximately 0.60 within error. In (ii), we find nu approximately 0.66, a value between the 3D and 2D (nu=3/4) exponents. Evidence is also presented for the localization of knot crossings in 2D under weak adsorption conditions.     

Anderson transition in two-dimensional systems with spin-orbit coupling

We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent nu for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyze the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent nu=2.73+/-0.02.     

Vortex glass transition in a frustrated 3D XY model with disorder

The anisotropic frustrated three-dimensional (3D) XY model with disorder in the coupling constants is simulated as a model of a point disordered superconductor in an applied magnetic field. A finite size scaling analysis of the helicity modulus gives strong evidence for a finite temperature transition with isotropic scaling and the correlation length exponent nu=1.5+/-0.3, consistent with 3D gauge glass universality.