Statistical mechanics of RNA folding: a lattice approach

We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA consists of just one hairpin. Using exact arguments and Monte Carlo simulations we determine the phase diagram for this case. We show that the denaturation transition is first order and can either occur directly or through an intermediate molten phase.Comment: 8 pages, 9 figure

Superconducting ``metals'' and ``insulators''

We propose a characterization of zero temperature phases in disordered superconductors on the basis of the nature of quasiparticle transport. In three dimensional systems, there are two distinct phases in close analogy to the distinction between normal metals and insulators: the superconducting "metal" with delocalized quasiparticle excitations and the superconducting "insulator" with localized quasiparticles. We describe experimental realizations of either phase, and study their general properties theoretically. We suggest experiments where it should be possible to tune from one superconducting phase to the other, thereby probing a novel "metal-insulator" transition inside a superconductor. We point out various implications of our results for the phase transitions where the superconductor is destroyed at zero temperature to form either a normal metal or a normal insulator.Comment: 18 page

Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples

We introduce a strong-disorder renormalization group (RG) approach suitable for investigating the quasiparticle excitations of disordered superconductors in which the quasiparticle spin is not conserved. We analyze one-dimensional models with this RG and with elementary transfer matrix methods. We find that such models with broken spin rotation invariance {\it generically} lie in one of two topologically distinct localized phases. Close enough to the critical point separating the two phases, the system has a power-law divergent low-energy density of states (with a non-universal continuously varying power-law) in either phase, due to quantum Griffiths singularities. This critical point belongs to the same infinite-disorder universality class as the one dimensional particle-hole symmetric Anderson localization problem, while the Griffiths phases in the vicinity of the transition are controlled by lines of strong (but not infinite) disorder fixed points terminating in the critical point.Comment: 14 pages (two-column PRB format), 9 eps figure

Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states

When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in the metallic phase violate the bound on such correlations that results from the reality of the Ising couplings. Some types of disorder in spinless or spin-polarized p-wave superconductors and paired fractional quantum Hall states allow a mapping onto an Ising model with real but correlated bonds, and hence a metallic phase is not possible there either. It is further argued that vortex disorder, which is generic in the fractional quantum Hall applications, destroys the ordered or weak-pairing phase, in which nonabelian statistics is obtained in the pure case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe

Fokker-Planck equations and density of states in disordered quantum wires

We propose a general scheme to construct scaling equations for the density of states in disordered quantum wires for all ten pure Cartan symmetry classes. The anomalous behavior of the density of states near the Fermi level for the three chiral and four Bogoliubov-de Gennes universality classes is analysed in detail by means of a mapping to a scaling equation for the reflection from a quantum wire in the presence of an imaginary potential.Comment: 10 pages, 5 figures, revised versio