Non-Ergodic Dynamics of the 2D Random-phase Sine-Gordon Model: Applications to Vortex-Glass Arrays and Disordered-Substrate Surfaces

The dynamics of the random-phase sine-Gordon model, which describes 2D vortex-glass arrays and crystalline surfaces on disordered substrates, is investigated using the self-consistent Hartree approximation. The fluctuation-dissipation theorem is violated below the critical temperature T_c for large time t>t* where t* diverges in the thermodynamic limit. While above T_c the averaged autocorrelation function diverges as Tln(t), for T<T_c it approaches a finite value q* proportional to 1/(T_c-T) as q(t) = q* - c(t/t*)^{-\nu} (for t --> t*) where \nu is a temperature-dependent exponent. On larger time scales t > t* the dynamics becomes non-ergodic. The static correlations behave as Tln{x} for T>T_c and for T<T_c when x < \xi* with \xi* proportional to exp{A/(T_c-T)}. For scales x > \xi*, they behave as (T/m)ln{x} where m is approximately T/T_c near T_c, in general agreement with the variational replica-symmetry breaking approach and with recent simulations of the disordered-substrate surface. For strong- coupling the transition becomes first-order.Comment: 12 pages in LaTeX, Figures available upon request, NSF-ITP 94-10

A variational study of the random-field XY model

A disorder-dependent Gaussian variational approach is applied to the $d$-dimensional ferromagnetic XY model in a random field. The randomness yields a non extensive contribution to the variational free energy, implying a random mass term in correlation functions. The Imry-Ma low temperature result, concerning the existence ($d>4$) or absence ($d < 4$) of long-range order is obtained in a transparent way. The physical picture which emerges below $d=4$ is that of a marginally stable mixture of domains. We also calculate within this variational scheme, disorder dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size.Comment: 14 pages, latex fil

Sliding Phases in XY-Models, Crystals, and Cationic Lipid-DNA Complexes

We predict the existence of a totally new class of phases in weakly coupled, three-dimensional stacks of two-dimensional (2D) XY-models. These ``sliding phases'' behave essentially like decoupled, independent 2D XY-models with precisely zero free energy cost associated with rotating spins in one layer relative to those in neighboring layers. As a result, the two-point spin correlation function decays algebraically with in-plane separation. Our results, which contradict past studies because we include higher-gradient couplings between layers, also apply to crystals and may explain recently observed behavior in cationic lipid-DNA complexes.Comment: 4 pages of double column text in REVTEX format and 1 postscript figur

The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

Hydrodynamics of the quantum Hall smectics

We propose a dynamical theory of the stripe phase arising in a two-dimensional electron liquid near half-integral fillings of high Landau levels. The system is modelled as a novel type of a smectic liquid crystal with the Lorentz force dominated dynamics. We calculate the structure factor, the dispersion relation of the collective modes (magnetophonons), and their intrinsic attenuation rate. We find strong power-law renormalizations of the elastic and dissipative coefficients by thermal fluctuations familiar from the conventional smectics but with different dynamical scaling exponents.Comment: Replaced with the published versio

Collective roughening of elastic lines with hard core interaction in a disordered environment

We investigate by exact optimization methods the roughening of two and three-dimensional systems of elastic lines with point disorder and hard-core repulsion with open boundary conditions. In 2d we find logarithmic behavior whereas in 3d simple random walk-like behavior. The line 'forests' become asymptotically completely entangled as the system height is increased at fixed line density due to increasing line wandering

Elastic Theory of pinned flux lattices

The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon=4-d)$, the functional renormalization group. We find universal logarithmic growth of displacements for $2<d<4$: $\overline{\langle u(x)-u(0) \rangle ^2}\sim A_d \log|x|$ and persistence of algebraic quasi-long range translational order. When the two methods can be compared they agree within $10\%$ on the value of $A_d$. We compute the function describing the crossover between the ``random manifold'' regime and the logarithmic regime. This crossover should be observable in present decoration experiments.Comment: 12 pages, Revtex 3.

Iterated Moire Maps and Braiding of Chiral Polymer Crystals

In the hexagonal columnar phase of chiral polymers a bias towards cholesteric twist competes with braiding along an average direction. When the chirality is strong, screw dislocations proliferate, leading to either a tilt grain boundary phase or a new "moire state" with twisted bond order. Polymer trajectories in the plane perpendicular to their average direction are described by iterated moire maps of remarkable complexity.Comment: 10 pages (plain tex) 3 figures uufiled and appende