Topological relaxation of entangled flux lattices: Single vs collective line dynamics

A symbolic language allowing to solve statistical problems for the systems with nonabelian braid-like topology in 2+1 dimensions is developed. The approach is based on the similarity between growing braid and "heap of colored pieces". As an application, the problem of a vortex glass transition in high-T_c superconductors is re-examined on microscopic levelComment: 4 pages (revtex), 4 figure

Comment on: Role of Intermittency in Urban Development: A Model of Large-Scale City Formation

Comment to D.H. Zanette and S.C. Manrubia, Phys. Rev. Lett. 79, 523 (1997).Comment: 1 page no figure

Non-perturbative renormalization of the KPZ growth dynamics

We introduce a non-perturbative renormalization approach which identifies stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of rough surfaces. The usual limitations of real space methods to deal with anisotropic (self-affine) scaling are overcome with an indirect functional renormalization. The roughness exponent $\alpha$ is computed for dimensions $d=1$ to 8 and it results to be in very good agreement with the available simulations. No evidence is found for an upper critical dimension. We discuss how the present approach can be extended to other self-affine problems.Comment: 4 pages, 2 figures. To appear in Phys. Rev. Let

Quantized Scaling of Growing Surfaces

The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should satisfy an operator product expansion and, unlike the correlations in a turbulent fluid, exhibit no multiscaling. These properties impose a quantization condition on the roughness exponent $\chi$ and the dynamic exponent $z$. Hence the exact values $\chi = 2/5, z = 8/5$ for two-dimensional and $\chi = 2/7, z = 12/7$ for three-dimensional surfaces are derived.Comment: 4 pages, revtex, no figure

Energy Barriers for Flux Lines in 3 Dimensions

I determine the scaling behavior of the free energy barriers encountered by a flux line in moving through a three-dimensional random potential. A combination of numerical simulations and analytic arguments suggest that these barriers scale with the length of the line in the same way as the fluctuation in the free energy.Comment: 12 pages Latex, 4 postscript figures tarred, compressed, uuencoded using `uufiles', coming with a separate fil

Quenched Averages for self-avoiding walks and polygons on deterministic fractals

We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W_n(S), and rooted self-avoiding polygons P_n(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P_n(S), and W_n(S) for an arbitrary point S on the lattice. These are used to compute the averages $, ,$ and $<log W_n(S)>$ over different positions of S. We find that the connectivity constant $\mu$, and the radius of gyration exponent $\nu$ are the same for the annealed and quenched averages. However, $~ n log \mu + (\alpha_q -2) log n$, and $~ n log \mu + (\gamma_q -1)log n$, where the exponents $\alpha_q$ and $\gamma_q$ take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives $\alpha_q \simeq 0.72837 \pm 0.00001$; and $\gamma_q \simeq 1.37501 \pm 0.00003$, to be compared with the annealed values $\alpha_a = 0.73421$ and $\gamma_a = 1.37522$.Comment: 17 pages, 10 figures, submitted to Journal of Statistical Physic

Generalized Dielectric Breakdown Model

We propose a generalized version of the Dielectric Breakdown Model (DBM) for generic breakdown processes. It interpolates between the standard DBM and its analog with quenched disorder, as a temperature like parameter is varied. The physics of other well known fractal growth phenomena as Invasion Percolation and the Eden model are also recovered for some particular parameter values. The competition between different growing mechanisms leads to new non-trivial effects and allows us to better describe real growth phenomena. Detailed numerical and theoretical analysis are performed to study the interplay between the elementary mechanisms. In particular, we observe a continuously changing fractal dimension as temperature is varied, and report an evidence of a novel phase transition at zero temperature in absence of an external driving field; the temperature acts as a relevant parameter for the ``self-organized'' invasion percolation fixed point. This permits us to obtain new insight into the connections between self-organization and standard phase transitions.Comment: Submitted to PR

Exact Large Deviation Function in the Asymmetric Exclusion Process

By an extension of the Bethe ansatz method used by Gwa and Spohn, we obtain an exact expression for the large deviation function of the time averaged current for the fully asymmetric exclusion process in a ring containing $N$ sites and $p$ particles. Using this expression we easily recover the exact diffusion constant obtained earlier and calculate as well some higher cumulants. The distribution of the deviation $y$ of the average current is, in the limit $N \to \infty$, skew and decays like $\exp - (A y^{5/2})$ for $y \to + \infty$ and $\exp - (A' |y|^{3/2})$ for $y \to -\infty$. Surprisingly, the large deviation function has an expression very similar to the pressure (as a function of the density) of an ideal Bose or Fermi gas in $3d$.Comment: 8 pages, in ReVTeX, e-mail addresses: [email protected] and [email protected]

Phase Transitions of the Flux Line Lattice in High-Temperature Superconductors with Weak Columnar and Point Disorder

We study the effects of weak columnar and point disorder on the vortex-lattice phase transitions in high temperature superconductors. The combined effect of thermal fluctuations and of quenched disorder is investigated using a simplified cage model. For columnar disorder the problem maps into a quantum particle in a harmonic + random potential. We use the variational approximation to show that columnar and point disorder have opposite effect on the position of the melting line as observed experimentally. Replica symmetry breaking plays a role at the transition into a vortex glass at low temperatures.Comment: 4 pages in 2 columns format + 2 eps figs included, uses RevTeX and multicol.st

Phase Separation in One-Dimensional Driven Diffusive Systems

A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the three densities are equal, it is shown that the model obeys detailed balance. The Hamiltonian governing the steady state distribution in this case is given and is found to have long range asymmetric interactions. The partition sum and bounds on some correlation functions are calculated analytically demonstrating phase separation.Comment: 4 Pages, Revtex, 2 Figures included, Submitted to Physical Review Letter