512 research outputs found
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
On the Treatment of Neutrino Oscillations Without Resort to Weak Eigenstates
We discuss neutrino oscillations in the framework of the quantum field theory
without introducing the concept of neutrino weak eigenstates. The external
particles are described by wave packets and the different mass eigenstate
neutrinos propagate between the production and detection interactions, which
are macroscopically localized in space-time. The time-averaged cross section,
which is the measurable quantity in the usual experimental setting, is
calculated. It is shown that only in the extremely relativistic limit the usual
quantum mechanical oscillation probability can be factored out of the cross
section.Comment: LaTeX-18pages, JHU-TIPAC-930011,DFTT 22/9
Infrared Evolution and Phase Structure of a Gauge Theory Containing Different Fermion Representations
We study the evolution of an asymptotically free vectorial SU() gauge
theory from the ultraviolet to the infrared and the resultant phase structure
in the general case in which the theory contains fermions transforming
according to several different representations of the gauge group. We discuss
the sequential fermion condensation and dynamical mass generation that occur,
and comment on the effect of bare fermion mass terms.Comment: 13 pages, late
Patterns of Dynamical Gauge Symmetry Breaking
We construct and analyze theories with a gauge symmetry in the ultraviolet of
the form , in which the vectorial, asymptotically free
gauge interaction becomes strongly coupled at a scale where the interaction
is weakly coupled and produces bilinear fermion condensates that dynamically
break the symmetry. Comparisons are given between Higgs and dynamical
symmetry breaking mechanisms for various models.Comment: 14 pages, late
Some Exact Results on the Potts Model Partition Function in a Magnetic Field
We consider the Potts model in a magnetic field on an arbitrary graph .
Using a formula of F. Y. Wu for the partition function of this model as a
sum over spanning subgraphs of , we prove some properties of concerning
factorization, monotonicity, and zeros. A generalization of the Tutte
polynomial is presented that corresponds to this partition function. In this
context we formulate and discuss two weighted graph-coloring problems. We also
give a general structural result for for cyclic strip graphs.Comment: 5 pages, late
Comparison of Some Exact and Perturbative Results for a Supersymmetric SU() Gauge Theory
We consider vectorial, asymptotically free supersymmetric
SU() gauge theories with copies of massless chiral super fields in
various representations and study how perturbative predictions for the lower
boundary of the infrared conformal phase, as a function of , compare with
exact results. We make use of two-loop and three-loop calculations of the beta
function and anomalous dimension of the quadratic chiral super field operator
product for this purpose. The specific chiral superfield contents that we
consider are copies of (i) , (ii) , (iii) ,
and (iv) , where , , , and denote,
respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2
tensor representations. We find that perturbative results slightly overestimate
the value of relative to the respective exact results for these
representations, i.e., slightly underestimate the interval in for which
the theory has infrared conformal behavior. Our results provide a measure of
how closely perturbative calculations reproduce exact results for these
theories.Comment: 16 pages, 3 figure
Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
We consider a vectorial, asymptotically free gauge theory and analyze the
effect of higher-loop corrections to the beta function on the evolution of the
theory from the ultraviolet to the infrared. We study the case in which the
theory contains copies of a fermion transforming according to the
fundamental representation and several higher-dimensional representations of
the gauge group. We also calculate higher-loop values of the anomalous
dimension of the mass, of at the infrared zero of the
beta function. We find that for a given theory, the values of
calculated to three- and four-loop order, and evaluated at the infrared zero
computed to the same order, tend to be somewhat smaller than the value
calculated to two-loop order. The results are compared with recent lattice
simulations.Comment: 22 pages, latex, matches Phys. Rev. D publicatio
Magnetothermodynamics: Measurements Of The Thermodynamic Properties In A Relaxed Magnetohydrodynamic Plasma
We have explored the thermodynamics of compressed magnetized plasmas in laboratory experiments and we call these studies ‘magnetothermodynamics’. The experiments are carried out in the Swarthmore Spheromak eXperiment device. In this device, a magnetized plasma source is located at one end and at the other end, a closed conducting can is installed. We generate parcels of magnetized plasma and observe their compression against the end wall of the conducting cylinder. The plasma parameters such as plasma density, temperature and magnetic field are measured during compression using HeNe laser interferometry, ion Doppler spectroscopy and a linear dot{B} probe array, respectively. To identify the instances of ion heating during compression, a PV diagram is constructed using measured density, temperature and a proxy for the volume of the magnetized plasma. Different equations of state are analysed to evaluate the adiabatic nature of the compressed plasma. A three-dimensional resistive magnetohydrodynamic code (NIMROD) is employed to simulate the twisted Taylor states and shows stagnation against the end wall of the closed conducting can. The simulation results are consistent to what we observe in our experiments
Simultaneous Extraction of the Fermi constant and PMNS matrix elements in the presence of a fourth generation
Several recent studies performed on constraints of a fourth generation of
quarks and leptons suffer from the ad-hoc assumption that 3 x 3 unitarity holds
for the first three generations in the neutrino sector. Only under this
assumption one is able to determine the Fermi constant G_F from the muon
lifetime measurement with the claimed precision of G_F = 1.16637 (1) x 10^-5
GeV^-2. We study how well G_F can be extracted within the framework of four
generations from leptonic and radiative mu and tau decays, as well as from K_l3
decays and leptonic decays of charged pions, and we discuss the role of lepton
universality tests in this context. We emphasize that constraints on a fourth
generation from quark and lepton flavour observables and from electroweak
precision observables can only be obtained in a consistent way if these three
sectors are considered simultaneously. In the combined fit to leptonic and
radiative mu and tau decays, K_l3 decays and leptonic decays of charged pions
we find a p-value of 2.6% for the fourth generation matrix element |U_{e 4}|=0
of the neutrino mixing matrix.Comment: 19 pages, 3 figures with 16 subfigures, references and text added
refering to earlier related work, figures and text in discussion section
added, results and conclusions unchange
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