The Number of Incipient Spanning Clusters in Two-Dimensional Percolation

Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.Comment: 9 pages, LaTeX, 1 eps figure. Additional references and comparison with existing numerical results include

Critical Exponents near a Random Fractal Boundary

The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension \xt. We consider the case when the boundary is a random fractal, specifically a self-avoiding walk or the frontier of a Brownian walk, in two dimensions, and show that the boundary scaling behaviour of the correlation function is characterised by a set of multifractal boundary exponents, given exactly by conformal invariance arguments to be \lambda_n = 1/48 (\sqrt{1+24n\xt}+11)(\sqrt{1+24n\xt}-1). This result may be interpreted in terms of a scale-dependent distribution of opening angles $\alpha$ of the fractal boundary: on short distance scales these are sharply peaked around $\alpha=\pi/3$. Similar arguments give the multifractal exponents for the case of coupling to a quenched random bulk geometry.Comment: 13 pages. Comments on relation to results in quenched random bulk added, and on relation to other recent work. Typos correcte

PERFORMANCE MEASURES: BANDWIDTH VERSUS FIDELITY IN PERFORMANCE MANAGEMENT

Performance is of focal and critical interest in organizations. Despite its criticality, when it comes to human performance there are many questions as to how to best measure and manage performance. One such issue is the breadth of the performance that should be considered. In this paper, we examine the issue of the breadth of performance in terms of measuring and managing performance. Overall, a contingency approach is taken in which the expected benefits and preference for broad or narrow performance measures depend on the type of job (fixed or changeable).bandwidth, fidelity in performance management, performance measures

Fermionic field theory for directed percolation in (1+1) dimensions

We formulate directed percolation in (1+1) dimensions in the language of a reaction-diffusion process with exclusion taking place in one space dimension. We map the master equation that describes the dynamics of the system onto a quantum spin chain problem. From there we build an interacting fermionic field theory of a new type. We study the resulting theory using renormalization group techniques. This yields numerical estimates for the critical exponents and provides a new alternative analytic systematic procedure to study low-dimensional directed percolation.Comment: 20 pages, 2 figure

Conformal Invariance in (2+1)-Dimensional Stochastic Systems

Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and some are indeed proved) to be described by conformal field theories. We advance, in the framework of the Martin-Siggia-Rose field theoretical formalism of stochastic dynamics, a general solution of the translation Ward identities, which yields a putative conformal energy-momentum tensor. Even though the computation of energy-momentum correlators is obstructed, in principle, by dimensional reduction issues, these are bypassed by the addition of replicated fields to the original (2+1)-dimensional model. The method is illustrated with an application to the Kardar-Parisi-Zhang (KPZ) model of surface growth. The consistency of the approach is checked by means of a straightforward perturbative analysis of the KPZ ultraviolet region, leading, as expected, to its $c=1$ conformal fixed point.Comment: Title, abstract and part of the text have been rewritten. To be published in Physical Review E

Integrable versus Non-Integrable Spin Chain Impurity Models

Recent renormalization group studies of impurities in spin-1/2 chains appear to be inconsistent with Bethe ansatz results for a special integrable model. We study this system in more detail around the integrable point in parameter space and argue that this integrable impurity model corresponds to a non-generic multi-critical point. Using previous results on impurities in half-integer spin chains, a consistent renormalization group flow and phase diagram is proposed.Comment: 20 pages 11 figures obtainable from authors, REVTEX 3.

Universal amplitudes in the FSS of three-dimensional spin models

In a MC study using a cluster update algorithm we investigate the finite-size scaling (FSS) of the correlation lengths of several representatives of the class of three-dimensional classical O(n) symmetric spin models on a column geometry. For all considered models we find strong evidence for a linear relation between FSS amplitudes and scaling dimensions when applying antiperiodic instead of periodic boundary conditions across the torus. The considered type of scaling relation can be proven analytically for systems on two-dimensional strips with periodic bc using conformal field theoryComment: 4 pages, RevTex, uses amsfonts.sty, 3 Figure

Kinetics of ballistic annihilation and branching

We consider a one-dimensional model consisting of an assembly of two-velocity particles moving freely between collisions. When two particles meet, they instantaneously annihilate each other and disappear from the system. Moreover each moving particle can spontaneously generate an offspring having the same velocity as its mother with probability 1-q. This model is solved analytically in mean-field approximation and studied by numerical simulations. It is found that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the slow dynamics of the system is governed by the coarsening of clusters of particles having the same velocities, while for q>1/2 the system relaxes rapidly towards its stationary state characterized by a distribution of small cluster sizes.Comment: 10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also avaiable at http://mykonos.unige.ch/~rey/pubt.htm

Complex noise in diffusion-limited reactions of replicating and competing species

We derive exact Langevin-type equations governing quasispecies dynamics. The inherent multiplicative noise has both real and imaginary parts. The numerical simulation of the underlying complex stochastic partial differential equations is carried out employing the Cholesky decomposition for the noise covariance matrix. This noise produces unavoidable spatio-temporal density fluctuations about the mean field value. In two dimensions, the fluctuations are suppressed only when the diffusion time scale is much smaller than the amplification time scale for the master species.Comment: 10 pages, 2 composite figure

Universal amplitude-exponent relation for the Ising model on sphere-like lattices

Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems $S^{d-1}\times\mathbb{R}$ of arbitrary dimensionality $d$. Numerical studies have up to now been unable to validate this result due to the intricacies of lattice discretisation of such curved spaces. We present a cluster-update Monte Carlo study of the Ising model on a three-dimensional geometry using slightly irregular lattices that confirms the validity of a linear amplitude-exponent relation to high precision.Comment: 6 pages, 2 figures, Europhys. Lett., in prin