Transconducting Transition for a Dynamic Boundary Coupled to Several Luttinger Liquids.

We study a dynamic boundary, e.g., a mobile impurity, coupled to N independent Tomonaga-Luttinger liquids (TLLs) each with interaction parameter K. We demonstrate that for N≥2 there is a quantum phase transition at K≥1/2, where the TLL phases lock together at the particle position, resulting in a nonzero transconductance equal to e^{2}/Nh. The transition line terminates for strong coupling at K=1-(1/N), consistent with results at large N. Another type of a dynamic boundary is a superconducting (or a Bose-Einstein condensate) grain coupled to N≥2 TLLs; here the transition signals also the onset of a relevant Josephson coupling.

Quantitative Scaling of Magnetic Avalanches.

We provide the first quantitative comparison between Barkhausen noise experiments and recent predictions from the theory of avalanches for pinned interfaces, both in and beyond mean field. We study different classes of soft magnetic materials, including polycrystals and amorphous samples-which are characterized by long-range and short-range elasticity, respectively-both for thick and thin samples, i.e., with and without eddy currents. The temporal avalanche shape at fixed size as well as observables related to the joint distribution of sizes and durations are analyzed in detail. Both long-range and short-range samples with no eddy currents are fitted extremely well by the theoretical predictions. In particular, the short-range samples provide the first reliable test of the theory beyond mean field. The thick samples show systematic deviations from the scaling theory, providing unambiguous signatures for the presence of eddy currents.

Disorder induced transitions in layered coulomb gases and superconductors

A 3D layered system of charges with logarithmic interaction parallel to the layers and random dipoles is studied via a novel variational method and an energy rationale which reproduces the known phase diagram for a single layer. Increasing interlayer coupling leads to successive transitions in which charge rods correlated in N>1 neighboring layers are nucleated by weaker disorder. For layered superconductors in the limit of only magnetic interlayer coupling, the method predicts and locates a disorder induced defect-unbinding transition in the flux lattice. While N = 1 charges dominate there, N>1 disorder induced defect rods are predicted for multilayer superconductors.

Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models.

We study via renormalization group (RG), numerics, exact bounds, and qualitative arguments the equilibrium Gibbs measure of a particle in a d-dimensional Gaussian random potential with translationally invariant logarithmic spatial correlations. We show that for any d>/=1 it exhibits a transition at T=T(c)>0. The low-temperature glass phase has a nontrivial structure, being dominated by a few distant states (with replica symmetry breaking phenomenology). In finite dimension this transition exists only in this "marginal glass" case (energy fluctuation exponent straight theta=0) and disappears if correlations grow faster (single ground-state dominance straight theta>0) or slower (high-temperature phase). The associated extremal statistics problem for correlated energy landscapes exhibits universal features which we describe using a nonlinear Kolmogorov (KPP) RG equation. These include the tails of the distribution of the minimal energy (or free energy) and the finite-size corrections, which are universal. The glass transition is closely related to Derrida's random energy models. In d=2, the connection between this problem and Liouville and sinh-Gordon models is discussed. The glass transition of the particle exhibits interesting similarities with the weak- to strong-coupling transition in Liouville (c=1 barrier) and with a transition that we conjecture for the sinh-Gordon model, with correspondence in some exact results and RG analysis. Glassy freezing of the particle is associated with the generation under RG of new local operators and of nonsmooth configurations in Liouville. Applications to Dirac fermions in random magnetic fields at criticality reveal a peculiar "quasilocalized" regime (corresponding to the glass phase for the particle), where eigenfunctions are concentrated over a finite number of distant regions, and allow us to recover the multifractal spectrum in the delocalized regime.

Exact multilocal renormalization group and applications to disordered problems.

We develop a method, the exact multilocal renormalization group (EMRG) which applies to a broad set of theories. It is based on the systematic multilocal expansion of the Polchinski-Wilson exact renormalization group (ERG) equation together with a scheme to compute correlation functions. Integrating out explicitly the nonlocal interactions, we reduce the ERG equation obeyed by the full interaction functional to a flow equation for a function, its local part. This is done perturbatively around fixed points, but exactly to any given order in the local part. It is thus controlled, at variance with projection methods, e.g., derivative expansions or local potential approximations. Our EMRG method is well-suited to problems such as the pinning of disordered elastic systems, previously described via functional renormalization group (FRG) approach based on a hard cutoff scheme. Since it involves arbitrary cutoff functions, we explicitly verify universality to O(epsilon=4-D), both of the T=0 FRG equation and of correlations. Extension to finite temperature T yields the finite size (L) susceptibility fluctuations characterizing mesoscopic behavior (Deltachi)2 approximately L(straight theta)/T, where straight theta is the energy exponent. Finally, we obtain the universal scaling function to O(epsilon(1/3)) which describes the ground state of a domain wall in a random field confined by a field gradient, compare with exact results and variational method. Explicit two loop exact RG equations are derived and the application to the FRG problem is sketched.

Nonequilibrium dynamics of random field Ising spin chains: exact results via real space renormalization group.

The nonequilibrium dynamics of classical random Ising spin chains with nonconserved magnetization are studied using an asymptotically exact real space renormalization group (RSRG). We focus on random field Ising model (RFIM) spin chains with and without a uniform applied field, as well as on Ising spin glass chains in an applied field. For the RFIM we consider a universal regime where the random field and the temperature are both much smaller than the exchange coupling. In this regime, the Imry-Ma length that sets the scale of the equilibrium correlations is large and the coarsening of domains from random initial conditions (e.g., a quench from high temperature) occurs over a wide range of length scales. The two types of domain walls that occur diffuse in opposite random potentials, of the form studied by Sinai, and domain walls annihilate when they meet. Using the RSRG we compute many universal asymptotic properties of both the nonequilibrium dynamics and the equilibrium limit. We find that the configurations of the domain walls converge rapidly toward a set of system-specific time-dependent positions that are independent of the initial conditions. Thus the behavior of this nonequilibrium system is pseudodeterministic at long times because of the broad distributions of barriers that occur on the long length scales involved. Specifically, we obtain the time dependence of the energy, the magnetization, and the distribution of domain sizes (found to be statistically independent). The equilibrium limits agree with known exact results. We obtain the exact scaling form of the two-point equal time correlation function and the two-time autocorrelations . We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the +/-J Ising spin glass in an applied field are obtained from the RFIM via a gauge transformation. In addition to these we compute the two-point two-time correlation function which can in principle be measured by experiments on spin-glass-like systems. The thermal fluctuations are studied and found to be dominated by rare events; in particular all moments of truncated equal time correlations are computed. Physical properties which are typically measured in aging experiments are also studied, focusing on the response to a small magnetic field which is applied after waiting for the system to equilibrate for a time t(w). The nonequilibrium fluctuation-dissipation ratio X(t,t(w)) is computed. We find that for (t-t(w)) approximately t(alpha)(w) with alpha;<1, the ratio equal to its equilibrium value X=1, although time translational invariance does not hold in this regime. For t-t(w) approximately t(w) the ratio exhibits an aging regime with a nontrivial X=X(t/t(w)) not equal to 1, but the behavior is markedly different from mean field theory. Finally the distribution of the total magnetization and of the number of domains is computed for large finite size systems. General issues about convergence toward equilibrium and the possibilities of weakly history-dependent evolution in other random systems are discussed.