15,168 research outputs found
The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion
For independent nearest-neighbour bond percolation on Z^d with d >> 6, we
prove that the incipient infinite cluster's two-point function and three-point
function converge to those of integrated super-Brownian excursion (ISE) in the
scaling limit. The proof is based on an extension of the new expansion for
percolation derived in a previous paper, and involves treating the magnetic
field as a complex variable. A special case of our result for the two-point
function implies that the probability that the cluster of the origin consists
of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an
error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong
statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic,
and xr package
Elastic Instabilities within Antiferromagnetically Ordered Phase in the Orbitally-Frustrated Spinel GeCoO
Ultrasound velocity measurements of the orbitally-frustrated GeCoO
reveal unusual elastic instabilities due to the phonon-spin coupling within the
antiferromagnetic phase. Shear moduli exhibit anomalies arising from the
coupling to short-range ferromagnetic excitations. Diplike anomalies in the
magnetic-field dependence of elastic moduli reveal magnetic-field-induced
orbital order-order transitions. These results strongly suggest the presence of
geometrical orbital frustration which causes novel orbital phenomena within the
antiferromagnetic phase.Comment: 5 pages, 3 figure
Theoretical study of the (3x2) reconstruction of beta-SiC(001)
By means of ab initio molecular dynamics and band structure calculations, as
well as using calculated STM images, we have singled out one structural model
for the (3x2) reconstruction of the Si-terminated (001) surface of cubic SiC,
amongst several proposed in the literature. This is an alternate dimer-row
model, with an excess Si coverage of 1/3, yielding STM images in good accord
with recent measurements [F.Semond et al. Phys. Rev. Lett. 77, 2013 (1996)].Comment: To be published in PRB Rapid. Com
On balanced complementation for regular t-wise balanced designs
AbstractVanstone has shown a procedure, called r-complementation, to construct a regular pairwise balanced design from an existing regular pairwise balanced design. In this paper, we give a generalization of r-complementation, called balanced complementation. Necessary and sufficient conditions for balanced complementation which gives a regular t-wise balanced design from an existing regular t-wise balanced design are shown. We characterize those aspects of designs which permit balanced complementation. Results obtained here will be applied to construct regular t-wise balanced designs which are useful in Statistics
New Lower Bounds on the Self-Avoiding-Walk Connective Constant
We give an elementary new method for obtaining rigorous lower bounds on the
connective constant for self-avoiding walks on the hypercubic lattice .
The method is based on loop erasure and restoration, and does not require exact
enumeration data. Our bounds are best for high , and in fact agree with the
first four terms of the expansion for the connective constant. The bounds
are the best to date for dimensions , but do not produce good results
in two dimensions. For , respectively, our lower bound is within
2.4\%, 0.43\%, 0.12\%, 0.044\% of the value estimated by series extrapolation.Comment: 35 pages, 388480 bytes Postscript, NYU-TH-93/02/0
Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model
The scaling behaviour of the edge of the Lee--Yang zeroes in the four
dimensional Ising model is analyzed. This model is believed to belong to the
same universality class as the model which plays a central role in
relativistic quantum field theory. While in the thermodynamic limit the scaling
of the Yang--Lee edge is not modified by multiplicative logarithmic
corrections, such corrections are manifest in the corresponding finite--size
formulae. The asymptotic form for the density of zeroes which recovers the
scaling behaviour of the susceptibility and the specific heat in the
thermodynamic limit is found to exhibit logarithmic corrections too. The
density of zeroes for a finite--size system is examined both analytically and
numerically.Comment: 17 pages (4 figures), LaTeX + POSTSCRIPT-file, preprint UNIGRAZ-UTP
20-11-9
On the measurement of the proton-air cross section using longitudinal shower profiles
In this paper, we will discuss the prospects of deducing the proton-air cross
section from fluorescence telescope measurements of extensive air showers. As
it is not possible to observe the point of first interaction
directly, other observables closely linked to must be inferred from
the longitudinal profiles. This introduces a dependence on the models used to
describe the shower development. The most straightforward candidate for a good
correlation to is the depth of shower maximum . We
will discuss the sensitivity of an -based analysis on and quantify the systematic uncertainties arising from the model
dependence, parameters of the reconstruction method itself and a possible
non-proton contamination of the selected shower sample.Comment: 4 pages, Proceedings for ISVHECRI Weihei 200
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