Is the Peak Value of σxx\sigma_{xx} at the Quantum Hall Transition Universal?

The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance $g$ is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity $\sigma_{xx}$ was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that $\sigma_{xx}$ is reduced by a factor $(1+g/2\pi)^{-1}$, at least for small $g$. This provides some theoretical evidence for the non-universality of $\sigma_{xx}$, as observed in a number of experiments.Comment: 2 double-column LaTeX pages, no figures, to appear in Z.Phys.

Critical behavior of weakly-disordered anisotropic systems in two dimensions

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent $\nu$ of the correlation length for the 3- and 4-state random-bond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in $\epsilon=c-\frac{1}{2}$ (with $c$ the central charge of the Potts model) and that the numerical values of $\nu$ are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3- and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.

The scaling behaviour of screened polyelectrolytes

We present a field-theoretic renormalization group (RG) analysis of a single flexible, screened polyelectrolyte chain (a Debye-H\"uckel chain) in a polar solvent. We point out that the Debye-H\"uckel chain may be mapped onto a local field theory which has the same fixed point as a generalised $n \to 1$ Potts model. Systematic analysis of the field theory shows that the system is one with two interplaying length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. To illustrate this, we solve the RG equation and explicitly calculate the exponents and the mean end-to-end length of the chain.Comment: 6 pages, 1 figure; changed title and slight modification to tex

Surface critical behavior in fixed dimensions d<4d<4: Nonanalyticity of critical surface enhancement and massive field theory approach

The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is investigated theoretically. The appropriate extension of Parisi's massive field theory approach is presented.Two-loop calculations and subsequent Pad\'e-Borel analyses of surface critical exponents of the special and ordinary phase transitions yield estimates in reasonable agreement with recent Monte Carlo results. This includes the crossover exponent $\Phi (d=3)$, for which we obtain the values $\Phi (n=1)\simeq 0.54$ and $\Phi (n=0)\simeq 0.52$, considerably lower than the previous $\epsilon$-expansion estimates.Comment: Latex with Revtex-Stylefiles, 4 page

Duality symmetry, strong coupling expansion and universal critical amplitudes in two-dimensional \Phi^{4} field models

We show that the exact beta-function \beta(g) in the continuous 2D g\Phi^{4} model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation \tilde{g}=d(g) such that \beta(d(g))=d'(g)\beta(g) is constructed and the approximate values of g^{*} computed from the duality equation d(g^{*})=g^{*} are shown to agree with the available numerical results. The calculation of the beta-function \beta(g) for the 2D scalar g\Phi^{4} field theory based on the strong coupling expansion is developed and the expansion of \beta(g) in powers of g^{-1} is obtained up to order g^{-8}. The numerical values calculated for the renormalized coupling constant g_{+}^{*} are in reasonable good agreement with the best modern estimates recently obtained from the high-temperature series expansion and with those known from the perturbative four-loop renormalization-group calculations. The application of Cardy's theorem for calculating the renormalized isothermal coupling constant g_{c} of the 2D Ising model and the related universal critical amplitudes is also discussed.Comment: 16 pages, REVTeX, to be published in J.Phys.A:Math.Ge

On the Finite Size Scaling in Disordered Systems

The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established and analyzed near the upper critical dimension $d=4-\epsilon$ and some universal results are obtained. The problem of self-averaging is clarified for different critical regimes.Comment: 21 pages, 2 figures, submitted to the Physcal Review

Characterization of the Local Density of States Fluctuations near the Integer Quantum Hall Transition in a Quantum Dot Array

We present a calculation for the second moment of the local density of states in a model of a two-dimensional quantum dot array near the quantum Hall transition. The quantum dot array model is a realistic adaptation of the lattice model for the quantum Hall transition in the two-dimensional electron gas in an external magnetic field proposed by Ludwig, Fisher, Shankar and Grinstein. We make use of a Dirac fermion representation for the Green functions in the presence of fluctuations for the quantum dot energy levels. A saddle-point approximation yields non-perturbative results for the first and second moments of the local density of states, showing interesting fluctuation behaviour near the quantum Hall transition. To our knowledge we discuss here one of the first analytic characterizations of chaotic behaviour for a two-dimensional mesoscopic structure. The connection with possible experimental investigations of the local density of states in the quantum dot array structures (by means of NMR Knight-shift or single-electron-tunneling techniques) and our work is also established.Comment: 11 LaTeX pages, 1 postscript figure, to appear in Phys.Rev.

The correction-to-scaling exponent in dilute systems

The leading correction-to-scaling exponent $\omega$ for the three-dimensional dilute Ising model is calculated in the framework of the field theoretic renormalization group approach. Both in the minimal subtraction scheme as well as in the massive field theory (resummed four loop expansion) excellent agreement with recent Monte Carlo calculations [Ballesteros H G, et al Phys. Rev. B 58, 2740 (1998)] is achieved. The expression of $\omega$ as series in a $\sqrt{\epsilon}$-expansion up to ${\cal O}(\epsilon^2)$ does not allow a reliable estimate for $d=3$.Comment: 4 pages, latex, 1 eps-figure include

Disordered Flat Phase and Phase Diagram for Restricted Solid on Solid Models of Fcc(110) Surfaces

We discuss the results of a study of restricted solid-on-solid models for fcc (110) surfaces. These models are simple modifications of the exactly solvable BCSOS model, and are able to describe a $(2\times 1)$ missing-row reconstructed surface as well as an unreconstructed surface. They are studied in two different ways. The first is by mapping the problem onto a quantum spin-1/2 one-dimensional hamiltonian of the Heisenberg type, with competing $S^z_iS^z_j$ couplings. The second is by standard Monte Carlo simulations. We find phase diagrams with the following features, which we believe to be quite generic: (i) two flat, ordered phases (unreconstructed and missing-row reconstructed); a rough, disordered phase; an intermediate disordered flat (DF) phase, characterized by monoatomic steps, whose physics is shown to be akin to that of a dimer spin state. (ii) a transition line from the $(2\times 1)$ reconstructed phase to the DF phase showing exponents which appear to be close, within our numerical accuracy, to the 2D-Ising universality class. (iii) a critical (preroughening) line with variable exponents, separating the unreconstructed phase from the DF phase. Possible signatures and order parameters of the DF phase are investigated.Comment: Revtex (22 pages) + 15 figures (uuencoded file

Advanced Technologies for Oral Controlled Release: Cyclodextrins for oral controlled release

Cyclodextrins (CDs) are used in oral pharmaceutical formulations, by means of inclusion complexes formation, with the following advantages for the drugs: (1) solubility, dissolution rate, stability and bioavailability enhancement; (2) to modify the drug release site and/or time profile; and (3) to reduce or prevent gastrointestinal side effects and unpleasant smell or taste, to prevent drug-drug or drug-additive interactions, or even to convert oil and liquid drugs into microcrystalline or amorphous powders. A more recent trend focuses on the use of CDs as nanocarriers, a strategy that aims to design versatile delivery systems that can encapsulate drugs with better physicochemical properties for oral delivery. Thus, the aim of this work was to review the applications of the CDs and their hydrophilic derivatives on the solubility enhancement of poorly water soluble drugs in order to increase their dissolution rate and get immediate release, as well as their ability to control (to prolong or to delay) the release of drugs from solid dosage forms, either as complexes with the hydrophilic (e.g. as osmotic pumps) and/ or hydrophobic CDs. New controlled delivery systems based on nanotechonology carriers (nanoparticles and conjugates) have also been reviewed