210 research outputs found
General solution of an exact correlation function factorization in conformal field theory
We discuss a correlation function factorization, which relates a three-point
function to the square root of three two-point functions. This factorization is
known to hold for certain scaling operators at the two-dimensional percolation
point and in a few other cases. The correlation functions are evaluated in the
upper half-plane (or any conformally equivalent region) with operators at two
arbitrary points on the real axis, and a third arbitrary point on either the
real axis or in the interior. This type of result is of interest because it is
both exact and universal, relates higher-order correlation functions to
lower-order ones, and has a simple interpretation in terms of cluster or loop
probabilities in several statistical models. This motivated us to use the
techniques of conformal field theory to determine the general conditions for
its validity.
Here, we discover a correlation function which factorizes in this way for any
central charge c, generalizing previous results. In particular, the
factorization holds for either FK (Fortuin-Kasteleyn) or spin clusters in the
Q-state Potts models; it also applies to either the dense or dilute phases of
the O(n) loop models. Further, only one other non-trivial set of highest-weight
operators (in an irreducible Verma module) factorizes in this way. In this case
the operators have negative dimension (for c < 1) and do not seem to have a
physical realization.Comment: 7 pages, 1 figure, v2 minor revision
The density of critical percolation clusters touching the boundaries of strips and squares
We consider the density of two-dimensional critical percolation clusters,
constrained to touch one or both boundaries, in infinite strips, half-infinite
strips, and squares, as well as several related quantities for the infinite
strip. Our theoretical results follow from conformal field theory, and are
compared with high-precision numerical simulation. For example, we show that
the density of clusters touching both boundaries of an infinite strip of unit
width (i.e. crossing clusters) is proportional to .
We also determine numerically contours for the density of clusters crossing
squares and long rectangles with open boundaries on the sides, and compare with
theory for the density along an edge.Comment: 11 pages, 6 figures. Minor revision
Exact results at the 2-D percolation point
We derive exact expressions for the excess number of clusters b and the
excess cumulants b_n of a related quantity at the 2-D percolation point.
High-accuracy computer simulations are in accord with our predictions. b is a
finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula
for the number of clusters per site n_c in the infinite system limit; the bn
correct bulk cumulants. b and b_n are universal, and thus depend only on the
system's shape. Higher-order corrections show no apparent dependence on
fractional powers of the system size.Comment: 12 pages, 2 figures, LaTeX, submitted to Physical Review Letter
Global Properties of Spherical Nuclei Obtained from Hartree-Fock-Bogoliubov Calculations with the Gogny Force
Selfconsistent Hartree-Fock-Bogoliubov (HFB) calculations have been performed
with the Gogny force for nuclei along several constant Z and constant N chains,
with the purpose of extracting the macroscopic part of the binding energy using
the Strutinsky prescription. The macroscopic energy obtained in this way is
compared to current liquid drop formulas. The evolution of the single particle
levels derived from the HFB calculations along the constant Z and constant N
chains and the variations of the different kinds of nuclear radii are also
analysed. Those radii are shown to follow isospin-dependent three parameter
laws close to the phenomenological formulas which reproduce experimental data.Comment: 17 pages in LaTeX and 17 figures in eps. Phys. Rev. C, accepted for
publicatio
Anchored Critical Percolation Clusters and 2-D Electrostatics
We consider the densities of clusters, at the percolation point of a
two-dimensional system, which are anchored in various ways to an edge. These
quantities are calculated by use of conformal field theory and computer
simulations. We find that they are given by simple functions of the potentials
of 2-D electrostatic dipoles, and that a kind of superposition {\it cum}
factorization applies. Our results broaden this connection, already known from
previous studies, and we present evidence that it is more generally valid. An
exact result similar to the Kirkwood superposition approximation emerges.Comment: 4 pages, 1 (color) figure. More numerics, minor corrections,
references adde
Tachyon condensation and off-shell gravity/gauge duality
We investigate quasilocal tachyon condensation by using gravity/gauge
duality. In order to cure the IR divergence due to a tachyon, we introduce two
regularization schemes: AdS space and a d=10 Schwarzschild black hole in a
cavity. These provide stable canonical ensembles and thus are good candidates
for the endpoint of tachyon condensation. Introducing the Cardy-Verlinde
formula, we establish the on-shell gravity/gauge duality. We propose that the
stringy geometry resulting from the off-shell tachyon dynamics matches onto the
off-shell AdS black hole, where "off-shell" means non-equilibrium
configuration. The instability induced by condensation of a tachyon behaves
like an off-shell black hole and evolves toward a large stable black hole. The
off-shell free energy and its derivative (-function) are used to show
the off-shell gravity/gauge duality for the process of tachyon condensation.
Further, d=10 Schwarzschild black hole in a cavity is considered for the
Hagedorn transition as a possible explanation of the tachyon condensation.Comment: 28 pages, 13 eps figures, version to appear in IJMP
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