156 research outputs found
Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings
We present exact results on the partition function of the -state Potts
model on various families of graphs in a generalized external magnetic
field that favors or disfavors spin values in a subset of
the total set of possible spin values, , where and are
temperature- and field-dependent Boltzmann variables. We remark on differences
in thermodynamic behavior between our model with a generalized external
magnetic field and the Potts model with a conventional magnetic field that
favors or disfavors a single spin value. Exact results are also given for the
interesting special case of the zero-temperature Potts antiferromagnet,
corresponding to a set-weighted chromatic polynomial that counts
the number of colorings of the vertices of subject to the condition that
colors of adjacent vertices are different, with a weighting that favors or
disfavors colors in the interval . We derive powerful new upper and lower
bounds on for the ferromagnetic case in terms of zero-field
Potts partition functions with certain transformed arguments. We also prove
general inequalities for on different families of tree graphs.
As part of our analysis, we elucidate how the field-dependent Potts partition
function and weighted-set chromatic polynomial distinguish, respectively,
between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur
Spontaneous Magnetization and Electron Momentum Density in 3D Quantum Dots
We discuss an exactly solvable model Hamiltonian for describing the
interacting electron gas in a quantum dot. Results for a spherical square well
confining potential are presented. The ground state is found to exhibit
striking oscillations in spin polarization with dot radius at a fixed electron
density. These oscillations are shown to induce characteristic signatures in
the momentum density of the electron gas, providing a novel route for direct
experimental observation of the dot magnetization via spectroscopies sensitive
to the electron momentum density.Comment: 5 pages (Revtex4), 4 (eps) figure
On the Crustal Matter of Magnetars
We have investigated some of the properties of dense sub-nuclear matter at
the crustal region (both the outer crust and the inner crust region) of a
magnetar. The relativistic version of Thomas-Fermi (TF) model is used in
presence of strong quantizing magnetic field for the outer crust matter. The
compressed matter in the outer crust, which is a crystal of metallic iron, is
replaced by a regular array of spherically symmetric Wigner-Seitz (WS) cells.
In the inner crust region, a mixture of iron and heavier neutron rich nuclei
along with electrons and free neutrons has been considered. Conventional
Harrison-Wheeler (HW) and Bethe-Baym-Pethick (BBP) equation of states are used
for the nuclear mass formula. A lot of significant changes in the
characteristic properties of dense crustal matter, both at the outer crust and
the inner crust, have been observed.Comment: 29 pages REVTEX manuscript, 15 .eps figures (included
Limits on the production of scalar leptoquarks from Z (0) decays at LEP
A search has been made for pairs and for single production of scalar leptoquarks of the first and second generations using a data sample of 392000 Z0 decays from the DELPHI detector at LEP 1. No signal was found and limits on the leptoquark mass, production cross section and branching ratio were set. A mass limit at 95% confidence level of 45.5 GeV/c2 was obtained for leptoquark pair production. The search for the production of a single leptoquark probed the mass region above this limit and its results exclude first and second generation leptoquarks D0 with masses below 65 GeV/c2 and 73 GeV/c2 respectively, at 95% confidence level, assuming that the D0lq Yukawa coupling alpha(lambda) is equal to the electromagnetic one. An upper limit is also given on the coupling alpha(lambda) as a function of the leptoquark mass m(D0)
Outsourcing Logistics or Running In-House: What Factors Influence a Company's Decision Making?
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