87 research outputs found
Exact results for the universal area distribution of clusters in percolation, Ising and Potts models
At the critical point in two dimensions, the number of percolation clusters
of enclosed area greater than A is proportional to 1/A, with a proportionality
constant C that is universal. We show theoretically (based upon Coulomb gas
methods), and verify numerically to high precision, that C = 1/(8 sqrt(3) pi) =
0.022972037.... We also derive, and verify to varying precision, the
corresponding constant for Ising spin clusters, and for Fortuin-Kasteleyn
clusters of the Q=2, 3 and 4-state Potts models.Comment: 42 pages, 9 figures, accepted for publication, J. Statis. Phy
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
Purely Transmitting Defect Field Theories
We define an infinite class of integrable theories with a defect which are
formulated as chiral defect perturbations of a conformal field theory. Such
theories can be interacting in the bulk, and are purely transmitting through
the defect. The examples of the sine-Gordon theory and Ising model are worked
out in some detail.Comment: 24 pages of Tex with harvmac macros; three references have been adde
Entanglement renormalization, scale invariance, and quantum criticality
The use of entanglement renormalization in the presence of scale invariance
is investigated. We explain how to compute an accurate approximation of the
critical ground state of a lattice model, and how to evaluate local
observables, correlators and critical exponents. Our results unveil a precise
connection between the multi-scale entanglement renormalization ansatz (MERA)
and conformal field theory (CFT). Given a critical Hamiltonian on the lattice,
this connection can be exploited to extract most of the conformal data of the
CFT that describes the model in the continuum limit.Comment: 4 pages, 3 figures, RevTeX 4. Revised for greater clarit
The Entanglement Entropy of Solvable Lattice Models
We consider the spin k/2 analogue of the XXZ quantum spin chain. We compute
the entanglement entropy S associated with splitting the infinite chain into
two semi-infinite pieces. In the scaling limit, we find S ~ c_k/6
(ln(xi))+ln(g)+... . Here xi is the correlation length and c_k=3k/(k+2) is the
central charge associated with the sl_2 WZW model at level k. ln(g) is the
boundary entropy of the WZW model. Our result extends previous observations and
suggests that this is a simple and perhaps rather general way both of
extracting the central charge of the ultraviolet CFT associated with the
scaling limit of a solvable lattice model, and of matching lattice and CFT
boundary conditions.Comment: 6 pages; connection with boundary entropy of Affleck and Ludwig added
in revised version and notation slightly change
Percolation Crossing Formulas and Conformal Field Theory
Using conformal field theory, we derive several new crossing formulas at the
two-dimensional percolation point. High-precision simulation confirms these
results. Integrating them gives a unified derivation of Cardy's formula for the
horizontal crossing probability , Watts' formula for the
horizontal-vertical crossing probability , and Cardy's formula for
the expected number of clusters crossing horizontally . The
main step in our approach implies the identification of the derivative of one
primary operator with another. We present operator identities that support this
idea and suggest the presence of additional symmetry in conformal field
theories.Comment: 12 pages, 5 figures. Numerics improved; minor correction
Shape-dependent universality in percolation
The shape-dependent universality of the excess percolation cluster number and
cross-configuration probability on a torus is discussed. Besides the aspect
ratio of the torus, the universality class depends upon the twist in the
periodic boundary conditions, which for example are generally introduced when
triangular lattices are used in simulations.Comment: 11 pages, 3 figures, to be published in Physica
Intermittency Studies in Directed Bond Percolation
The self-similar cluster fluctuations of directed bond percolation at the
percolation threshold are studied using techniques borrowed from
inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical
simulations based on the factorial moments for large -dimensional lattices
allow to handle statistical and boundary effects and show the existence of weak
but definite intermittency patterns. The extracted fractal dimensions are in
agreement with scaling arguments leading to a new relation linking the
intermittency indices to the critical exponents and the fractal dimension of
directed percolation clusters.Comment: 16pp. Geneva preprint UGVA-DPT 1992/06/769, Saclay preprint
SPhT/92-069 (to appear in Nucl. Phys. B[FS]
Difference Equations in Spin Chains with a Boundary
Correlation functions and form factors in vertex models or spin chains are
known to satisfy certain difference equations called the quantum
Knizhnik-Zamolodchikov equations. We find similar difference equations for the
case of semi-infinite spin chain systems with integrable boundary conditions.
We derive these equations using the properties of the vertex operators and the
boundary vacuum state, or alternatively through corner transfer matrix
arguments for the 8-vertex model with a boundary. The spontaneous boundary
magnetization is found by solving such difference equations. The boundary
-matrix is also proposed and compared, in the sine-Gordon limit, with
Ghoshal--Zamolodchikov's result. The axioms satisfied by the form factors in
the boundary theory are formulated.Comment: 28 pages, LaTeX with amssymbols.sty, 7 uuencoded postscript figure
Excess number of percolation clusters on the surface of a sphere
Monte Carlo simulations were performed in order to determine the excess
number of clusters b and the average density of clusters n_c for the
two-dimensional "Swiss cheese" continuum percolation model on a planar L x L
system and on the surface of a sphere. The excess number of clusters for the L
x L system was confirmed to be a universal quantity with a value b = 0.8841 as
previously predicted and verified only for lattice percolation. The excess
number of clusters on the surface of a sphere was found to have the value b =
1.215(1) for discs with the same coverage as the flat critical system. Finally,
the average critical density of clusters was calculated for continuum systems
n_c = 0.0408(1).Comment: 13 pages, 2 figure
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