Aging in the glass phase of a 2D random periodic elastic system

Using RG we investigate the non-equilibrium relaxation of the (Cardy-Ostlund) 2D random Sine-Gordon model, which describes pinned arrays of lines. Its statics exhibits a marginal ($\theta=0$) glass phase for $T<T_g$ described by a line of fixed points. We obtain the universal scaling functions for two-time dynamical response and correlations near $T_g$ for various initial conditions, as well as the autocorrelation exponent. The fluctuation dissipation ratio is found to be non-trivial and continuously dependent on $T$.Comment: 5 pages, RevTex, Modified Versio

Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets

Using the functional renormalization group (FRG) we study the thermal fluctuations of elastic objects, described by a displacement field u and internal dimension d, pinned by a random potential at low temperature T, as prototypes for glasses. A challenge is how the field theory can describe both typical (minimum energy T=0) configurations, as well as thermal averages which, at any non-zero T as in the phenomenological droplet picture, are dominated by rare degeneracies between low lying minima. We show that this occurs through an essentially non-perturbative *thermal boundary layer* (TBL) in the (running) effective action Gamma[u] at T>0 for which we find a consistent scaling ansatz to all orders. The TBL resolves the singularities of the T=0 theory and contains rare droplet physics. The formal structure of this TBL is explored around d=4 using a one loop Wilson RG. A more systematic Exact RG (ERG) method is employed and tested on d=0 models. There we obtain precise relations between TBL quantities and droplet probabilities which are checked against exact results. We illustrate how the TBL scaling remains consistent to all orders in higher d using the ERG and how droplet picture results can be retrieved. Finally, we solve for d=0,N=1 the formidable "matching problem" of how this T>0 TBL recovers a critical T=0 field theory. We thereby obtain the beta-function at T=0, *all ambiguities removed*, displayed here up to four loops. A discussion of d>4 case and an exact solution at large d are also provided

Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG

Non-equilibrium dynamics of classical random Ising spin chains are studied using asymptotically exact real space renormalization group. Specifically the random field Ising model with and without an applied field (and the Ising spin glass (SG) in a field), in the universal regime of a large Imry Ma length so that coarsening of domains after a quench occurs over large scales. Two types of domain walls diffuse in opposite Sinai random potentials and mutually annihilate. The domain walls converge rapidly to a set of system-specific time-dependent positions {\it independent of the initial conditions}. We obtain the time dependent energy, magnetization and domain size distribution (statistically independent). The equilibrium limits agree with known exact results. We obtain exact scaling forms for two-point equal time correlation and two-time autocorrelations. We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the spin glass are obtained. We compute the two-point two-time correlation which can be measured by experiments on spin-glass like systems. Thermal fluctuations are found to be dominated by rare events; all moments of truncated correlations are computed. The response to a small field applied after waiting time $t_w$, as measured in aging experiments, and the fluctuation-dissipation ratio $X(t,t_w)$ are computed. For $(t-t_w) \sim t_w^{\hat{\alpha}}$, $\hat{\alpha} <1$, it equals its equilibrium value X=1, though time translational invariance fails. It exhibits for $t-t_w \sim t_w$ aging regime with non-trivial $X=X(t/t_w) \neq 1$, different from mean field.Comment: 55 pages, 9 figures, revte

Disorder chaos in spin glasses

We investigate numerically disorder chaos in spin glasses, i.e. the sensitivity of the ground state to small changes of the random couplings. Our study focuses on the Edwards-Anderson model in d=1,2,3 and in mean-field. We find that in all cases, simple scaling laws, involving the size of the system and the strength of the perturbation, are obeyed. We characterize in detail the distribution of overlap between ground states and the geometrical properties of flipped spin clusters in both the weak and strong chaos regime. The possible relevance of these results to temperature chaos is discussed.Comment: 7 pages, 8 figures, replaced with accepted versio

Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?

Domain walls for spin glasses are believed to be scale invariant invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to test the hypothesis that these domain walls are described by a Schramm-Loewner evolution SLE$_\kappa$. Multiple tests are consistent with SLE$_\kappa$, where $\kappa=2.30(5)$. Both conformal invariance and the domain Markov property are tested. The latter does not hold in small systems, but detailed numerical evidence suggests that it holds in the continuum limit.Comment: 4 pages, 3 figures, see related work by Amoruso, Hartmann, Hastings, Moore at cond-mat/060171

Ground state properties of solid-on-solid models with disordered substrates

We study the glassy super-rough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a newly developed minimum cost flow algorithm. Results for the height-height correlation function are compared with analytical and numerical predictions. The domain wall energy of a boundary induced step grows logarithmically with system size, indicating the marginal stability of the ground state, and the fractal dimension of the step is estimated. The sensibility of the ground state with respect to infinitesimal variations of the quenched disorder is analyzed.Comment: 4 pages RevTeX, 3 eps-figures include

Glassy trapping of manifolds in nonpotential random flows

We study the dynamics of polymers and elastic manifolds in non potential static random flows. We find that barriers are generated from combined effects of elasticity, disorder and thermal fluctuations. This leads to glassy trapping even in pure barrier-free divergenceless flows $v {f \to 0}{\sim} f^\phi$ ($\phi > 1$). The physics is described by a new RG fixed point at finite temperature. We compute the anomalous roughness $R \sim L^\zeta$ and dynamical $t\sim L^z$ exponents for directed and isotropic manifolds.Comment: 5 pages, 3 figures, RevTe

Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments

Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of it not returning to the origin are obtained, as well as the two-time distribution which exhibits "aging" with $\frac{\ln t}{\ln t'}$ scaling and a singularity at $\ln t =\ln t'$. The effects of a small uniform force are also studied. Extension to motion of many domain walls yields non-equilibrium time dependent correlations for the 1D random field Ising model with Glauber dynamics and "persistence" exponents of 1D reaction-diffusion models with random forces.Comment: 5 pages, 1 figures, RevTe

Non-trivial fixed point structure of the two-dimensional +-J 3-state Potts ferromagnet/spin glass

The fixed point structure of the 2D 3-state random-bond Potts model with a bimodal ($\pm$J) distribution of couplings is for the first time fully determined using numerical renormalization group techniques. Apart from the pure and T=0 critical fixed points, two other non-trivial fixed points are found. One is the critical fixed point for the random-bond, but unfrustrated, ferromagnet. The other is a bicritical fixed point analogous to the bicritical Nishimori fixed point found in the random-bond frustrated Ising model. Estimates of the associated critical exponents are given for the various fixed points of the random-bond Potts model.Comment: 4 pages, 2 eps figures, RevTex 3.0 format requires float and epsfig macro