Dynamical scaling at the quantum Hall transition: Coulomb blockade versus phase breaking

We argue that the finite temperature dynamics of the integer quantum Hall system is governed by two independent length scales. The consistent scaling description of the transition makes crucial use of two temperature critical exponents, reflecting the interplay between charging effects and interaction-induced dephasing. Experimental implications of the two-scale picture are discussed.Comment: 4 pages, RevTeX, 1 figure included, minor changes, accepted in PR

Disorder and Quantum Fluctuations in Superconducting Films in Strong Magnetic Fields

We find that the upper critical field in a two-dimensional disordered superconductor can increase essentially at low temperatures. This happens due to the formation of local superconducting islands weakly coupled via the Josephson effect. The distribution of the superconducting islands is derived. It is shown that the value of the critical field is determined by the interplay of the proximity effect and quantum phase fluctuations. We find that the shift of the upper critical field is connected with the pinning properties of a superconductor.Comment: 4 page

Effect of screening of the Coulomb interaction on the conductivity in the quantum Hall regime

We study variable range hopping in the quantum Hall effect regime in the presence of a metallic gate parallel to the plane of a two-dimensional electron gas. Screening of the Coulomb interaction by the gate causes the partial ``filling'' of the Coulomb gap in the density of localized states. At low enough temperatures this leads to a substantial enhancement and a new temperature behavior of the hopping conductivity. As a result, the diagonal conductivity peaks become much wider. The power law dependence of the width of the peaks on the temperature changes: the corresponding exponent turns out to be twice as small as that for gateless structures. The width dependences on the current in non-ohmic regime and on the frequency for the absorption of the electromagnetic waves experience a similar modification. The experimental observation of the crossovers predicted may demonstrate the important role of the Coulomb interaction in the integer quantum Hall regime.Comment: 14 pages + 3 figures by request preprint TPI-MINN-93/58-

Exact renormalization-group analysis of first order phase transitions in clock models

We analyze the exact behavior of the renormalization group flow in one-dimensional clock-models which undergo first order phase transitions by the presence of complex interactions. The flow, defined by decimation, is shown to be single-valued and continuous throughout its domain of definition, which contains the transition points. This fact is in disagreement with a recently proposed scenario for first order phase transitions claiming the existence of discontinuities of the renormalization group. The results are in partial agreement with the standard scenario. However in the vicinity of some fixed points of the critical surface the renormalized measure does not correspond to a renormalized Hamiltonian for some choices of renormalization blocks. These pathologies although similar to Griffiths-Pearce pathologies have a different physical origin: the complex character of the interactions. We elucidate the dynamical reason for such a pathological behavior: entire regions of coupling constants blow up under the renormalization group transformation. The flows provide non-perturbative patterns for the renormalization group behavior of electric conductivities in the quantum Hall effect.Comment: 13 pages + 3 ps figures not included, TeX, DFTUZ 91.3

Dirichlet sigma models and mean curvature flow

The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renormalization group equation of Dirichlet sigma models away from conformality, to lowest order in perturbation theory. D-branes appear as fixed points of this flow having conformally invariant boundary conditions. Simple running solutions include the paper-clip and the hair-pin (or grim-reaper) models on the plane, as well as scaling solutions associated to rational (p, q) closed curves and the decay of two intersecting lines. Stability analysis is performed in several cases while searching for transitions among different brane configurations. The combination of Ricci with the mean curvature flow is examined in detail together with several explicit examples of deforming curves on curved backgrounds. Some general aspects of the mean curvature flow in higher dimensional ambient spaces are also discussed and obtain consistent truncations to lower dimensional systems. Selected physical applications are mentioned in the text, including tachyon condensation in open string theory and the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure

Scaling Theory of the Integer Quantum Hall Effect

The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finite-size scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localization-delocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.Comment: 96 pages, REVTeX 3, 28 figures, Figs. 8-24, 26-28 appended as uuencoded compressed tarred PostScript files. Submitted to Rev. Mod. Phys