Thermodynamic Fingerprints of Disorder in Flux Line Lattices and other Glassy Mesoscopic Systems

We examine probability distributions for thermodynamic quantities in finite-sized random systems close to criticality. Guided by available exact results, a general ansatz is proposed for replicated free energies, which leads to scaling forms for cumulants of various macroscopic observables. For the specific example of a planar flux line lattice in a two dimensional superconducting film near H_c1, we provide detailed results for the statistics of the magnetic flux density, susceptibility, heat capacity, and their cross-correlations.Comment: 4 page

Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.Comment: 4 pages, 4 figure

Dislocations in the ground state of the solid-on-solid model on a disordered substrate

We investigate the effects of topological defects (dislocations) to the ground state of the solid-on-solid (SOS) model on a simple cubic disordered substrate utilizing the min-cost-flow algorithm from combinatorial optimization. The dislocations are found to destabilize and destroy the elastic phase, particularly when the defects are placed only in partially optimized positions. For multi defect pairs their density decreases exponentially with the vortex core energy. Their mean distance has a maximum depending on the vortex core energy and system size, which gives a fractal dimension of $1.27 \pm 0.02$. The maximal mean distances correspond to special vortex core energies for which the scaling behavior of the density of dislocations change from a pure exponential decay to a stretched one. Furthermore, an extra introduced vortex pair is screened due to the disorder-induced defects and its energy is linear in the vortex core energy.Comment: 6 pages RevTeX, eps figures include

Topological Defects and the Spin Glass Phase of Cuprates

We propose that the spin glass phase of cuprates is due to the proliferation of topological defects of a spiral distortion of the antiferromagnet order. Our theory explains straightforwardly the simultaneous existence of short range incommensurate magnetic correlations and complete a-b symmetry breaking in this phase. We show via a renormalization group calculation that the collinear O(3)/O(2) symmetry is unstable towards the formation of local non-collinear correlations. A critical disorder strength is identified beyond which topological defects proliferate already at zero temperature.Comment: 7 pages, 2 figures. Final version with some changes and one replaced figur

Random pinning limits the size of membrane adhesion domains

Theoretical models describing specific adhesion of membranes predict (for certain parameters) a macroscopic phase separation of bonds into adhesion domains. We show that this behavior is fundamentally altered if the membrane is pinned randomly due to, e.g., proteins that anchor the membrane to the cytoskeleton. Perturbations which locally restrict membrane height fluctuations induce quenched disorder of the random-field type. This rigorously prevents the formation of macroscopic adhesion domains following the Imry-Ma argument [Y. Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975)]. Our prediction of random-field disorder follows from analytical calculations, and is strikingly confirmed in large-scale Monte Carlo simulations. These simulations are based on an efficient composite Monte Carlo move, whereby membrane height and bond degrees of freedom are updated simultaneously in a single move. The application of this move should prove rewarding for other systems also.Comment: revised and extended versio

Measuring functional renormalization group fixed-point functions for pinned manifolds

Exact numerical minimization of interface energies is used to test the functional renormalization group (FRG) analysis for interfaces pinned by quenched disorder. The fixed-point function R(u) (the correlator of the coarse-grained disorder) is computed. In dimensions D=d+1, a linear cusp in R''(u) is confirmed for random bond (d=1,2,3), random field (d=0,2,3), and periodic (d=2,3) disorders. The functional shocks that lead to this cusp are seen. Small, but significant, deviations from 1-loop FRG results are compared to 2-loop corrections. The cross-correlation for two copies of disorder is compared with a recent FRG study of chaos.Comment: 4 pages, 4 figure

Critical behavior of colloid-polymer mixtures in random porous media

We show that the critical behavior of a colloid-polymer mixture inside a random porous matrix of quenched hard spheres belongs to the universality class of the random-field Ising model. We also demonstrate that random-field effects in colloid-polymer mixtures are surprisingly strong. This makes these systems attractive candidates to study random-field behavior experimentally.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let

Fluids with quenched disorder: Scaling of the free energy barrier near critical points

In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, $P_L(m)$ becomes scale invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of $P_L(m)$ at the peaks ($P_{L, max}$) and the value at the minimum in-between ($P_{L, min}$) becomes $L$-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead $\Delta F_L := \ln (P_{L, max} / P_{L, min}) \propto L^\theta$ should be observed, where $\theta>0$ is the "violation of hyperscaling" exponent. Since $\theta$ is substantially non-zero, the scaling of $\Delta F_L$ with system size should be easily detectable in simulations. For two fluid models with quenched disorder, $\Delta F_L$ versus $L$ was measured, and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random-field Ising model.Comment: sent to J. Phys. Cond. Mat

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

On Integrable Doebner-Goldin Equations

We suggest a method for integrating sub-families of a family of nonlinear {\sc Schr\"odinger} equations proposed by {\sc H.-D.~Doebner} and {\sc G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie} symmetries. Since the method of integration involves non-local transformations of dependent and independent variables, general solutions obtained include implicitly determined functions. By properly specifying one of the arbitrary functions contained in these solutions, we obtain broad classes of explicit square integrable solutions. The physical significance and some analytical properties of the solutions obtained are briefly discussed.Comment: 23 pages, revtex, 1 figure, uses epsfig.sty and amssymb.st