Universality and Crossover of Directed Polymers and Growing Surfaces

We study KPZ surfaces on Euclidean lattices and directed polymers on hierarchical lattices subject to different distributions of disorder, showing that universality holds, at odds with recent results on Euclidean lattices. Moreover, we find the presence of a slow (power-law) crossover toward the universal values of the exponents and verify that the exponent governing such crossover is universal too. In the limit of a 1+epsilon dimensional system we obtain both numerically and analytically that the crossover exponent is 1/2.Comment: LateX file + 5 .eps figures; to appear on Phys. Rev. Let

VELO Module Production - Module Assembly

This note describes in detail the procedures used in the gluing of sensors to hybrid and hybrid to pedestal for the LHCb VELO detector module assembly

Numerical Results for the Ground-State Interface in a Random Medium

The problem of determining the ground state of a $d$-dimensional interface embedded in a $(d+1)$-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energy exponent being $\theta = 0.84 \pm 0.03, 1.45 \pm 0.04$, in $d = 2, 3$, respectively. These results are compared with previous analytical and numerical estimates.Comment: 10 pages, REVTEX3.0; 3 ps files (separate:tar/gzip/uuencoded) for figure

Elastic Chain in a Random Potential: Simulation of the Displacement Function <(u(x)−u(0))2><(u(x)-u(0))^2> and Relaxation

We simulate the low temperature behaviour of an elastic chain in a random potential where the displacements $u(x)$ are confined to the {\it longitudinal} direction ($u(x)$ parallel to $x$) as in a one dimensional charge density wave--type problem. We calculate the displacement correlation function $g(x)=< (u(x)-u(0))^2>$ and the size dependent average square displacement $W(L)=$. We find that $g(x)\sim x^{2\eta}$ with $\eta\simeq3/4$ at short distances and $\eta\simeq3/5$ at intermediate distances. We cannot resolve the asymptotic long distance dependence of $g$ upon $x$. For the system sizes considered we find $g(L/2)\propto W\sim L^{2\chi}$ with $\chi\simeq2/3$. The exponent $\eta\simeq3/5$ is in agreement with the Random Manifold exponent obtained from replica calculations and the exponent $\chi\simeq2/3$ is consistent with an exact solution for the chain with {\it transverse} displacements ($u(x)$ perpendicular to $x$).The distribution of nearest distances between pinning wells and chain-particles is found to develop forbidden regions.Comment: 19 pages of LaTex, 6 postscript figures available on request, submitted to Journal of Physics A, MAJOR CHANGE

Superconducting Phase with Fractional Vortices in the Frustrated Kagome Wire Network at f=1/2

In classical XY kagome antiferromagnets, there can be a novel low temperature phase where $\psi^3=e^{i3\theta}$ has quasi-long-range order but $\psi$ is disordered, as well as more conventional antiferromagnetic phases where $\psi$ is ordered in various possible patterns ($\theta$ is the angle of orientation of the spin). To investigate when these phases exist in a physical system, we study superconducting kagome wire networks in a transverse magnetic field when the magnetic flux through an elementary triangle is a half of a flux quantum. Within Ginzburg-Landau theory, we calculate the helicity moduli of each phase to estimate the Kosterlitz-Thouless (KT) transition temperatures. Then at the KT temperatures, we estimate the barriers to move vortices and effects that lift the large degeneracy in the possible $\psi$ patterns. The effects we have considered are inductive couplings, non-zero wire width, and the order-by-disorder effect due to thermal fluctuations. The first two effects prefer $q=0$ patterns while the last one selects a $\sqrt{3}\times\sqrt{3}$ pattern of supercurrents. Using the parameters of recent experiments, we conclude that at the KT temperature, the non-zero wire width effect dominates, which stabilizes a conventional superconducting phase with a $q=0$ current pattern. However, by adjusting the experimental parameters, for example by bending the wires a little, it appears that the novel $\psi^3$ superconducting phase can instead be stabilized. The barriers to vortex motion are low enough that the system can equilibrate into this phase.Comment: 30 pages including figure

Replica field theory and renormalization group for the Ising spin glass in an external magnetic field

We use the generic replica symmetric cubic field-theory to study the transition of short range Ising spin glasses in a magnetic field around the upper critical dimension, d=6. A novel fixed-point is found, in addition to the well-known zero magnetic field fixed-point, from the application of the renormalization group. In the spin glass limit, n going to 0, this fixed-point governs the critical behaviour of a class of systems characterised by a single cubic interaction parameter. For this universality class, the spin glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, the so-called anomalous one, however, behaves unusually, having a jump at criticality. The physical consequences of this unusual behaviour are discussed, and a comparison with the conventional de Almeida-Thouless scenario presented.Comment: 5 pages written in revtex4. Accepted for publication in Phys. Rev. Let

Residual Energies after Slow Quantum Annealing

Features of the residual energy after the quantum annealing are investigated. The quantum annealing method exploits quantum fluctuations to search the ground state of classical disordered Hamiltonian. If the quantum fluctuation is reduced sufficiently slowly and linearly by the time, the residual energy after the quantum annealing falls as the inverse square of the annealing time. We show this feature of the residual energy by numerical calculations for small-sized systems and derive it on the basis of the quantum adiabatic theorem.Comment: 4 pages, 2 figure

Extremal statistics in the energetics of domain walls

We study at T=0 the minimum energy of a domain wall and its gap to the first excited state concentrating on two-dimensional random-bond Ising magnets. The average gap scales as $\Delta E_1 \sim L^\theta f(N_z)$, where $f(y) \sim [\ln y]^{-1/2}$, $\theta$ is the energy fluctuation exponent, $L$ length scale, and $N_z$ the number of energy valleys. The logarithmic scaling is due to extremal statistics, which is illustrated by mapping the problem into the Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of domain walls has also a logarithmic dependence on system size.Comment: Accepted for publication in Phys. Rev.

Non-universal exponents in interface growth

We report on an extensive numerical investigation of the Kardar-Parisi-Zhang equation describing non-equilibrium interfaces. Attention is paid to the dependence of the growth exponents on the details of the distribution of the noise. All distributions considered are delta-correlated in space and time, and have finite cumulants. We find that the exponents become progressively more sensitive to details of the distribution with increasing dimensionality. We discuss the implications of these results for the universality hypothesis.Comment: 12 pages, 5 figures; to appear in Phys. Rev. Let