776,012 research outputs found
K0 form factor at order p^6 of chiral perturbation theory
This paper describes the calculation of the electromagnetic form factor of
the K0 meson at order p^6 of chiral perturbation theory which is the
next-to-leading order correction to the well-known p^4 result achieved by
Gasser and Leutwyler. On the one hand, at order p^6 the chiral expansion
contains 1- and 2-loop diagrams which are discussed in detail. Especially, a
numerical procedure for calculating the irreducible 2-loop graphs of the sunset
topology is presented. On the other hand, the chiral Lagrangian L^6 produces a
direct coupling of the K0 current with the electromagnetic field tensor. Due to
this coupling one of the unknown parameters of L^6 occurs in the contribution
to the K0 charge radius.Comment: 22 pages Latex with 8 figures, Typos corrected, one reference adde
Stiffness Exponents for Lattice Spin Glasses in Dimensions d=3,...,6
The stiffness exponents in the glass phase for lattice spin glasses in
dimensions are determined. To this end, we consider bond-diluted
lattices near the T=0 glass transition point . This transition for
discrete bond distributions occurs just above the bond percolation point
in each dimension. Numerics suggests that both points, and , seem to
share the same -expansion, at least for several leading orders, each
starting with . Hence, these lattice graphs have average connectivities
of near and exact graph-reduction methods become
very effective in eliminating recursively all spins of connectivity ,
allowing the treatment of lattices of lengths up to L=30 and with up to
spins. Using finite-size scaling, data for the defect energy width
over a range of in each dimension can be combined to
reach scaling regimes of about one decade in the scaling variable
. Accordingly, unprecedented accuracy is obtained for the
stiffness exponents compared to undiluted lattices (), where scaling is
far more limited. Surprisingly, scaling corrections typically are more benign
for diluted lattices. We find in for the stiffness exponents
, , and . The result for the
upper critical dimension, , suggest a mean-field value of .Comment: 8 pages, RevTex, 15 ps-figures included (see
http://www.physics.emory.edu/faculty/boettcher for related information
Graphs with Diameter Minimizing the Spectral Radius
The spectral radius of a graph is the largest eigenvalue of its
adjacency matrix . For a fixed integer , let be
a graph with minimal spectral radius among all connected graphs on vertices
with diameter . Let be a tree
obtained from a path of vertices () by
linking one pendant path at for each . For
, were determined in the literature.
Cioab\v{a}-van Dam-Koolen-Lee \cite{CDK} conjectured for fixed ,
is in the family . For , they conjectured
and
. In this paper, we settle
their three conjectures positively. We also determine in this
paper
Star-graph expansions for bond-diluted Potts models
We derive high-temperature series expansions for the free energy and the
susceptibility of random-bond -state Potts models on hypercubic lattices
using a star-graph expansion technique. This method enables the exact
calculation of quenched disorder averages for arbitrary uncorrelated coupling
distributions. Moreover, we can keep the disorder strength as well as the
dimension as symbolic parameters. By applying several series analysis
techniques to the new series expansions, one can scan large regions of the
parameter space for any value of . For the bond-diluted 4-state
Potts model in three dimensions, which exhibits a rather strong first-order
phase transition in the undiluted case, we present results for the transition
temperature and the effective critical exponent as a function of
as obtained from the analysis of susceptibility series up to order 18. A
comparison with recent Monte Carlo data (Chatelain {\em et al.}, Phys. Rev.
E64, 036120(2001)) shows signals for the softening to a second-order transition
at finite disorder strength.Comment: 8 pages, 6 figure
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