68,708 research outputs found
Acyclic orientations on the Sierpinski gasket
We study the number of acyclic orientations on the generalized
two-dimensional Sierpinski gasket at stage with equal to
two and three, and determine the asymptotic behaviors. We also derive upper
bounds for the asymptotic growth constants for and -dimensional
Sierpinski gasket .Comment: 20 pages, 8 figures and 6 table
Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips
We determine the general structure of the partition function of the -state
Potts model in an external magnetic field, for arbitrary ,
temperature variable , and magnetic field variable , on cyclic, M\"obius,
and free strip graphs of the square (sq), triangular (tri), and honeycomb
(hc) lattices with width and arbitrarily great length . For the
cyclic case we prove that the partition function has the form ,
where denotes the lattice type, are specified
polynomials of degree in , is the corresponding
transfer matrix, and () for ,
respectively. An analogous formula is given for M\"obius strips, while only
appears for free strips. We exhibit a method for
calculating for arbitrary and give illustrative
examples. Explicit results for arbitrary are presented for
with and . We find very simple formulas
for the determinant . We also give results for
self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W
Repulsive Fermions in Optical Lattices: Phase separation versus Coexistence of Antiferromagnetism and d-Superfluidity
We investigate a system of fermions on a two-dimensional optical square
lattice in the strongly repulsive coupling regime. In this case, the
interactions can be controlled by laser intensity as well as by Feshbach
resonance. We compare the energetics of states with resonating valence bond
d-wave superfluidity, antiferromagnetic long range order and a homogeneous
state with coexistence of superfluidity and antiferromagnetism. We show that
the energy density of a hole has a minimum at doping that
signals phase separation between the antiferromagnetic and d-wave paired
superfluid phases. The energy of the phase-separated ground state is however
found to be very close to that of a homogeneous state with coexisting
antiferromagnetic and superfluid orders. We explore the dependence of the
energy on the interaction strength and on the three-site hopping terms and
compare with the nearest neighbor hopping {\it t-J} model
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
Vacuum Energy Density and Cosmological Constant in dS Brane World
We discuss the vacuum energy density and the cosmological constant of dS
brane world with a dilaton field. It is shown that a stable AdS brane can
be constructed and gravity localization can be realized. An explicit relation
between the dS bulk cosmological constant and the brane cosmological constant
is obtained. The discrete mass spectrum of the massive scalar field in the
AdS brane is used to acquire the relationship between the brane
cosmological constant and the vacuum energy density. The vacuum energy density
in the brane gotten by this method is in agreement with astronomical
observations.Comment: 16 pages,4 figure
Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice
We present exact solutions for the zero-temperature partition function of the
-state Potts antiferromagnet (equivalently, the chromatic polynomial ) on
tube sections of the simple cubic lattice of fixed transverse size and arbitrarily great length , for sizes and and boundary conditions (a) and (b)
, where () denote free (periodic) boundary
conditions. In the limit of infinite-length, , we calculate the
resultant ground state degeneracy per site (= exponent of the ground-state
entropy). Generalizing from to , we determine
the analytic structure of and the related singular locus which
is the continuous accumulation set of zeros of the chromatic polynomial. For
the limit of a given family of lattice sections, is
analytic for real down to a value . We determine the values of
for the lattice sections considered and address the question of the value of
for a -dimensional Cartesian lattice. Analogous results are presented
for a tube of arbitrarily great length whose transverse cross section is formed
from the complete bipartite graph .Comment: 28 pages, latex, six postscript figures, two Mathematica file
Geometric CP Violation with Extra Dimensions
We discuss how CP symmetry can be broken geometrically through orbifold
projections in hidden extra dimensions in the context of D-brane models for
particle unifications. We present a few toy models to illustrate the idea and
suggest ways to incorporate this technique in the context of realistic models.Comment: 6 pages, one figure; references updated and a new model adde
Little Higgs Models and Precision Electroweak Data
We study the low energy limit of Little Higgs models. The method consists in
eliminating the heavy fields using their classical equations of motion in the
infinite mass limit. After the elimination of the heavy degrees of freedom we
can directly read off deviations from the precision electroweak data. We also
examine the effects on the low energy precision experiments.Comment: Misprint in eps3 for the custodial model corrected and additional
discussion of the triplet higg
The Decays to -wave Charmonium by Improved Bethe-Salpeter Approach
We re-calculate the exclusive semileptonic and nonleptonic decays of
meson to a -wave charmonium in terms of the improved Bethe-Salpeter (B-S)
approach, which is developed recently. Here the widths for the exclusive
semileptonic and nonleptonic decays, the form factors, and the charged lepton
spectrums for the semileptonic decays are precisely calculated. To test the
concerned approach by comparing with experimental measurements when the
experimental data are available, and to have comparisons with the other
approaches the results obtained by the approach and those by some approaches
else as well as the original B-S approach, which appeared in literature, are
comparatively presented and discussed.Comment: 33 pages, 5 figures, 3 table
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