782 research outputs found

    Scaling behaviour of lattice animals at the upper critical dimension

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    We perform numerical simulations of the lattice-animal problem at the upper critical dimension d=8 on hypercubic lattices in order to investigate logarithmic corrections to scaling there. Our stochastic sampling method is based on the pruned-enriched Rosenbluth method (PERM), appropriate to linear polymers, and yields high statistics with animals comprised of up to 8000 sites. We estimate both the partition sums (number of different animals) and the radii of gyration. We re-verify the Parisi-Sourlas prediction for the leading exponents and compare the logarithmic-correction exponents to two partially differing sets of predictions from the literature. Finally, we propose, and test, a new Parisi-Sourlas-type scaling relation appropriate for the logarithmic-correction exponents.Comment: 10 pages, 5 figure

    Correlated disordered interactions on Potts models

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    Using a weak-disorder scheme and real-space renormalization-group techniques, we obtain analytical results for the critical behavior of various q-state Potts models with correlated disordered exchange interactions along d1 of d spatial dimensions on hierarchical (Migdal-Kadanoff) lattices. Our results indicate qualitative differences between the cases d-d1=1 (for which we find nonphysical random fixed points, suggesting the existence of nonperturbative fixed distributions) and d-d1>1 (for which we do find acceptable perturbartive random fixed points), in agreement with previous numerical calculations by Andelman and Aharony. We also rederive a criterion for relevance of correlated disorder, which generalizes the usual Harris criterion.Comment: 8 pages, 4 figures, to be published in Physical Review

    Scaling properties in off equilibrium dynamical processes

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    In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations C(t,t)C(t,t'). We show, under general conditions, that C(t,t)C(t,t') must obey the following scaling behavior C(t,t)=ϕ1(t)f(β)S(β)C(t,t') = \phi_1(t)^{f(\beta)}{\cal{S}}(\beta), where the scaling variable is β=β(ϕ1(t)/ϕ1(t))\beta=\beta(\phi_1(t')/\phi_1(t)) and ϕ1(t)\phi_1(t'), ϕ1(t)\phi_1(t) two undetermined functions. The presence of a non constant exponent f(β)f(\beta) signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure

    Distribution of the area enclosed by a 2D random walk in a disordered medium

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    The asymptotic probability distribution for a Brownian particle wandering in a 2D plane with random traps to enclose the algebraic area A by time t is calculated using the instanton technique.Comment: 4 pages, ReVTeX. Phys. Rev. E (March 1999), to be publishe

    Frustrated two-dimensional Josephson junction array near incommensurability

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    To study the properties of frustrated two-dimensional Josephson junction arrays near incommensurability, we examine the current-voltage characteristics of a square proximity-coupled Josephson junction array at a sequence of frustrations f=3/8, 8/21, 0.382 ((35)/2)(\approx (3-\sqrt{5})/2), 2/5, and 5/12. Detailed scaling analyses of the current-voltage characteristics reveal approximately universal scaling behaviors for f=3/8, 8/21, 0.382, and 2/5. The approximately universal scaling behaviors and high superconducting transition temperatures indicate that both the nature of the superconducting transition and the vortex configuration near the transition at the high-order rational frustrations f=3/8, 8/21, and 0.382 are similar to those at the nearby simple frustration f=2/5. This finding suggests that the behaviors of Josephson junction arrays in the wide range of frustrations might be understood from those of a few simple rational frustrations.Comment: RevTex4, 4 pages, 4 eps figures, to appear in Phys. Rev.

    Methane in underground air in Gibraltar karst

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    AbstractLittle is known about the abundance and geochemical behaviour of gaseous methane in the unsaturated zone of karst terrains. The concentrations and δ13C of methane in background atmosphere, soil air and cave air collected at monthly intervals over a 4yr period are reported for St. Michaels Cave, Gibraltar, where the regional climate, surface and cave processes are well documented. Methane concentrations measured in Gibraltar soil are lower than the local background atmosphere average of 1868ppb and fall to <500ppb. The abundance–δ13C relationships in soil air methane lack strong seasonality and suggest mixing between atmosphere and a 12C depleted residue after methanotrophic oxidation. Methane abundances in cave air are also lower than the local background atmosphere average but show strong seasonality that is related to ventilation-controlled annual cycles shown by CO2. Cave air methane abundances are lowest in the CO2-rich air that outflows from cave entrances during the winter and show strong inverse relationship between CH4 abundance and δ13C which is diagnostic of methanotrophy within the cave and unsaturated zone. Anomalies in the soil and cave air seasonal patterns characterised by transient elevated CH4 mixing ratios with δ13C values lower than −47‰ suggests intermittent biogenic input. Dynamically ventilated Gibraltar caves may act as a net sink for atmospheric methane

    Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem

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    We study mode-locking in disordered media as a boundary-value problem. Focusing on the simplest class of mode-locking models which consists of a single driven overdamped degree-of-freedom, we develop an analytical method to obtain the shape of the Arnol'd tongues in the regime of low ac-driving amplitude or high ac-driving frequency. The method is exact for a scalloped pinning potential and easily adapted to other pinning potentials. It is complementary to the analysis based on the well-known Shapiro's argument that holds in the perturbative regime of large driving amplitudes or low driving frequency, where the effect of pinning is weak.Comment: 6 pages, 7 figures, RevTeX, Submitte

    Replica Symmetry Breaking Instability in the 2D XY model in a random field

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    We study the 2D vortex-free XY model in a random field, a model for randomly pinned flux lines in a plane. We construct controlled RG recursion relations which allow for replica symmetry breaking (RSB). The fixed point previously found by Cardy and Ostlund in the glass phase T<TcT<T_c is {\it unstable} to RSB. The susceptibility χ\chi associated to infinitesimal RSB perturbation in the high-temperature phase is found to diverge as χ(TTc)γ\chi \propto (T-T_c)^{-\gamma} when TTc+T \rightarrow T_c^{+}. This provides analytical evidence that RSB occurs in finite dimensional models. The physical consequences for the glass phase are discussed.Comment: 8 pages, REVTeX, LPTENS-94/2

    Smeared phase transition in a three-dimensional Ising model with planar defects: Monte-Carlo simulations

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    We present results of large-scale Monte Carlo simulations for a three-dimensional Ising model with short range interactions and planar defects, i.e., disorder perfectly correlated in two dimensions. We show that the phase transition in this system is smeared, i.e., there is no single critical temperature, but different parts of the system order at different temperatures. This is caused by effects similar to but stronger than Griffiths phenomena. In an infinite-size sample there is an exponentially small but finite probability to find an arbitrary large region devoid of impurities. Such a rare region can develop true long-range order while the bulk system is still in the disordered phase. We compute the thermodynamic magnetization and its finite-size effects, the local magnetization, and the probability distribution of the ordering temperatures for different samples. Our Monte-Carlo results are in good agreement with a recent theory based on extremal statistics.Comment: 9 pages, 6 eps figures, final version as publishe

    Drag forces on inclusions in classical fields with dissipative dynamics

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    We study the drag force on uniformly moving inclusions which interact linearly with dynamical free field theories commonly used to study soft condensed matter systems. Drag forces are shown to be nonlinear functions of the inclusion velocity and depend strongly on the field dynamics. The general results obtained can be used to explain drag forces in Ising systems and also predict the existence of drag forces on proteins in membranes due to couplings to various physical parameters of the membrane such as composition, phase and height fluctuations.Comment: 14 pages, 7 figure
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