Multilevel Tunnelling Systems and Fractal Clustering in the Low-Temperature Mixed Alkali-Silicate Glasses

The thermal and dielectric anomalies of window-type glasses at low temperatures ($T<$ 1 K) are rather successfully explained by the two-level systems (2LS) standard tunneling model (STM). However, the magnetic effects discovered in the multisilicate glasses in recent times, magnetic effects in the organic glasses and also some older data from mixed (SiO$_2$)$_{1-x}$(K$_2$O)$_x$ and (SiO$_2$)$_{1-x}$(Na$_2$O)$_x$ glasses indicate the need for a suitable extension of the 2LS-STM. We show that -- not only for the magnetic effects, but already for the mixed glasses in the absence of a field -- the right extension of the 2LS STM is provided by the (anomalous) multilevel tunnelling systems (A-TS) proposed by one of us for multicomponent amorphous solids. Though a secondary type of TS, different from the standard 2LS, was invoked long ago already, we clarify their physical origin and mathematical description and show that their contribution considerably improves the agreement with the experimental data.Comment: 20 pages, 15 figures (submitted for publication

On the Paramagnetic Impurity Concentration of Silicate Glasses from Low-Temperature Physics

The concentration of paramagnetic trace impurities in glasses can be determined via precise SQUID measurements of the sample's magnetization in a magnetic field. However the existence of quasi-ordered structural inhomogeneities in the disordered solid causes correlated tunneling currents that can contribute to the magnetization, surprisingly, also at the higher temperatures. We show that taking into account such tunneling systems gives rise to a good agreement between the concentrations extracted from SQUID magnetization and those extracted from low-temperature heat capacity measurements. Without suitable inclusion of such magnetization contribution from the tunneling currents we find that the concentration of paramagnetic impurities gets considerably over-estimated. This analysis represents a further positive test for the structural inhomogeneity theory of the magnetic effects in the cold glasses.Comment: 27 pages, 11 figures, 10 tables, 41 references: submitted to Journal of Low Temperature Physic

Tails of Localized Density of States of Two-dimensional Dirac Fermions

The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in the regime where all states are localized. We make use of a weak-disorder expansion in the parameter g/m^2, where g is the strength of disorder and m the average Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non-uniform solutions of the saddle point equation. The resulting density of states has tails which deviate from the typical pure Gaussian form by an analytic prefactor.Comment: 8 pages, REVTeX, 1 eps figure; to appear in Annalen der Physi

Quantized Transport in Two-Dimensional Spin-Ordered Structures

We study in detail the transport properties of a model of conducting electrons in the presence of double-exchange between localized spins arranged on a 2D Kagome lattice, as introduced by Ohgushi, Murakami, and Nagaosa (2000). The relationship between the canting angle of the spin texture $\theta$ and the Berry phase field flux per triangular plaquette $\phi$ is derived explicitly and we emphasize the similarities between this model and Haldane's honeycomb lattice version of the quantum Hall effect (Haldane, 1988). The quantization of the transverse (Hall) conductivity $\sigma_{xy}$ is derived explicitly from the Kubo formula and a direct calculation of the longitudinal conductivity $\sigma_{xx}$ shows the existence of a metal-insulator transition as a function of the canting angle $\theta$ (or flux density $\phi$). This transition might be linked to that observable in the manganite compounds or in the pyrochlore ones, as the spin ordering changes from ferromagnetic to canted.Comment: 17 pages, 12 figure

Spin-size disorder model for granular superconductors with charging effects

A quantum pseudo-spin model with random spin sizes is introduced to study the effects of charging-energy disorder on the superconducting transition in granular superconducting materials. Charging-energy effects result from the small electrical capacitance of the grains when the Coulomb charging energy is comparable to the Josephson coupling energy. In the pseudo-spin model, randomness in the spin size is argued to arise from the inhomogeneous grain-size distribution. For a particular bimodal spin-size distribution, the model describes percolating granular superconductors. A mean-field theory is developed to obtain the phase diagram as a function of temperature, average charging energy and disorder.Comment: 4 pages, 2 figure

Microscopic Oscillations in the Quantum Nucleation of Vortices Subject to Periodic Pinning Potential in a Thin Superconductor

We present a theory for the decay of a supercurrent through nucleation of vortex-antivortex pairs in a two-dimensional superconductor in the presence of dissipation and of a periodic pinning potential. Through a powerful quantum electrodynamics formulation of the problem we show that the nucleation rate develops oscillations in its current-density dependence which are connected to the pinning periodicity. A remnant of the dissipation-driven localization transition is present, and an estimate of the nucleation rate suggests that these effects might be observable in real thin superconductors.Comment: REVTeX file, 4 pages in two-column mode, 1 Postscript figure, to appear in Phys.Rev.B (Rapid Communications

Realistic Tunneling States for the Magnetic Effects in Non-Metallic Real Glasses

The discovery of magnetic and compositional effects in the low temperature properties of multi-component glasses has prompted the need to extend the standard two-level systems (2LSs) tunneling model. A possible extension \cite{Jug2004} assumes that a subset of tunneling quasi-particles is moving in a three-welled potential (TWP) associated with the ubiquitous inhomogeneities of the disordered atomic structure of the glass. We show that within an alternative, cellular description of the intermediate-range atomic structure of glasses the tunneling TWP can be fully justified. We then review how the experimentally discovered magnetic effects can be explained within the approach where only localized atomistic tunneling 2LSs and quasi-particles tunneling in TWPs are allowed. We discuss the origin of the magnetic effects in the heat capacity, dielectric constant (real and imaginary parts), polarization echo and SQUID magnetization in several glassy systems. We conclude by commenting on a strategy to reveal the mentioned tunneling states (2LSs and TWPs) by means of atomistic computer simulations and discuss the microscopic nature of the tunneling states in the context of the potential energy landscape of glass-forming systems.Comment: 48 pages, 27 figures; mini-review for the Proceedings of the XIV International Workshop on Complex Systems (Fai della Paganella, Trento, March 2015) (submitted to Phil.Mag.). arXiv admin note: text overlap with arXiv:cond-mat/0210221 by other author

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

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.