409 research outputs found
Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals
We prove a general rigorous lower bound for
, the exponent of the ground state
entropy of the -state Potts antiferromagnet, on an arbitrary Archimedean
lattice . We calculate large- series expansions for the exact
and compare these with our lower bounds on
this function on the various Archimedean lattices. It is shown that the lower
bounds coincide with a number of terms in the large- expansions and hence
serve not just as bounds but also as very good approximations to the respective
exact functions for large on the various lattices
. Plots of are given, and the general dependence on
lattice coordination number is noted. Lower bounds and series are also
presented for the duals of Archimedean lattices. As part of the study, the
chromatic number is determined for all Archimedean lattices and their duals.
Finally, we report calculations of chromatic zeros for several lattices; these
provide further support for our earlier conjecture that a sufficient condition
for to be analytic at is that is a regular
lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in
Phys. Rev.
A Non-Perturbative Analysis of the Finite T Phase Transition in SU(2)xU(1) Electroweak Theory
The continuum 3d SU(2)U(1)+Higgs theory is an effective theory for a
large class of 4d high-temperature gauge theories, including the minimal
standard model and some of its supersymmetric extensions. We study the effects
of the U(1) subgroup using lattice Monte Carlo techniques. When is
increased from the zero corresponding to pure SU(2)+Higgs theory, the phase
transition gets stronger. However, the increase in the strength is close to
what is expected perturbatively, and the qualitative features of the phase
diagram remain the same as for . In particular, the first order
transition still disappears for . We measure the photon mass and
mixing angle, and find that the mass vanishes in both phases within the
statistical errors.Comment: Latex, 30 pages, 15 eps figure
On a Neutrino Electroweak Radius
We study a combination of amplitudes for neutrino scattering that can isolate
a (gauge-invariant) difference of chirality-preserving neutrino electroweak
radii for and . This involves both photon and
exchange contributions. It is shown that the construction singles out the
contributions of the hypercharge gauge field in the standard model.
We comment on how gauge-dependent terms from the charge radii cancel with other
terms in the relative electroweak radii defined.Comment: 16 pages, revtex with embedded figure
High-Precision Entropy Values for Spanning Trees in Lattices
Shrock and Wu have given numerical values for the exponential growth rate of
the number of spanning trees in Euclidean lattices. We give a new technique for
numerical evaluation that gives much more precise values, together with
rigorous bounds on the accuracy. In particular, the new values resolve one of
their questions.Comment: 7 pages. Revision mentions alternative approach. Title changed
slightly. 2nd revision corrects first displayed equatio
A New Model for Fermion Masses in Supersymmetric Grand Unified Theories
We present a simple model for fermion mass matrices and quark mixing in the
context of supersymmetric grand unified theories and show its agreement with
experiment. Our model realizes the GUT mass relations , , in a new way and is easily consistent with values of
suggested by MSSM fits to LEP data.Comment: Latex, 8 p., ITP-SB-93-37 (revised version contains minor changes in
some wording and citations; no changes in analytic or numerical results.
Fermion Masses and Mixing in Extended Technicolor Models
We study fermion masses and mixing angles, including the generation of a
seesaw mechanism for the neutrinos, in extended technicolor (ETC) theories. We
formulate an approach to these problems that relies on assigning right-handed
quarks and charged leptons to ETC representations that are conjugates
of those of the corresponding left-handed fermions. This leads to a natural
suppression of these masses relative to the quarks, as well as the
generation of quark mixing angles, both long-standing challenges for ETC
theories. Standard-model-singlet neutrinos are assigned to ETC representations
that provide a similar suppression of neutrino Dirac masses, as well as the
possibility of a realistic seesaw mechanism with no mass scale above the
highest ETC scale of roughly TeV. A simple model based on the ETC group
SU(5) is constructed and analyzed. This model leads to non-trivial, but not
realistic mixing angles in the quark and lepton sectors. It can also produce
sufficiently light neutrinos, although not simultaneously with a realistic
quark spectrum. We discuss several aspects of the phenomenology of this class
of models.Comment: 74 pages, revtex with embedded figure
Limits on the Neutrino Mass and Mixing Angle from Pion and Lepton Decays
Motivated by a recent rather surprising conclusion based on the 1992 PDG data
on the pion, kaon and lepton decays that if three generations of neutrinos are
assumed to be massive and mixed, the heaviest neutrino, , could have a
mass in the range, 155~\mbox{MeV} \lsim m_3 \lsim 225~\mbox{MeV}, we have
analyzed the latest 1995 data on the leptonic decays of pion, and
with the assumption that three generations of neutrinos are massive and mixed.
It is shown that when the radiative corrections are included and the constraint
{}from partial decay widths is imposed, the 1995 data are consistent with three
massless neutrinos with no mixing. Various limits on the neutrino mass and
mixing angle implied by the 1995 data are presented together with a critique of
the previous analysis.Comment: REVTeX file, 20 pages and 10 figures (not included). Revision of the
analysis and inclusion of the latest data. The TeX file and the figures
(uuencoded, compressed, tarred file) are available at
http://fermi.pha.jhu.edu/personnel/fornengo/fornengo.htm
Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to
the study of the three-dimensional antiferromagnetic q-state Potts models on a
simple cubic lattice. We systematically study the phase transition of the
models with q=3, 4, 5 and 6. We obtain the finite-temperature phase transition
for q= 3 and 4, whereas the transition temperature is down to zero for q=5. For
q=6 there exists no order for all the temperatures. We also study the
ground-state properties. The size-dependence of the ground-state entropy is
investigated. We find that the ground-state entropy is larger than the
contribution from the typical configurations of the broken-sublattice-symmetry
state for q=3. The same situations are found for q = 4, 5 and 6.Comment: 9 pages including 9 eps figures, RevTeX, to appear in J. Phys.
q-Plane Zeros of the Potts Partition Function on Diamond Hierarchical Graphs
We report exact results concerning the zeros of the partition function of the Potts model in the complex q-plane, as a function of a temperature-like Boltzmann variable v, for the m-th iterate graphs Dm of the diamond hierarchical lattice, including the limit m → ∞. In this limit, we denote the continuous accumulation locus of zeros in the q-planes at fixed v = v0 as ℬ(0). We apply theorems from complex dynamics to establish the properties of ℬ(0). For v = −1 (the zero-temperature Potts antiferromagnet or, equivalently, chromatic polynomial), we prove that ℬ(−1) crosses the real q-axis at (i) a minimal point q = 0, (ii) a maximal point q = 3, (iii) q = 32/27, (iv) a cubic root that we give, with the value q = q1 = 1.638 896 9…, and (v) an infinite number of points smaller than q1, converging to 32/27 from above. Similar results hold for ℬ(0) for any −1 0 (Potts ferromagnet). We also provide the computer-generated plots of ℬ(0) at various values of v0 in both the antiferromagnetic and ferromagnetic regimes and compare them to the numerically computed zeros of Z(D4, q, v0)
Monte Carlo study of the antiferromagnetic three-state Potts model with staggered polarization field on the square lattice
Using the Wang-Landau Monte Carlo method, we study the antiferromagnetic (AF)
three-state Potts model with a staggered polarization field on the square
lattice. We obtain two phase transitions; one belongs to the ferromagnetic
three-state Potts universality class, and the other to the Ising universality
class. The phase diagram obtained is quantitatively consistent with the
transfer matrix calculation. The Ising transition in the large nearest-neighbor
interaction limit has been made clear by the detailed analysis of the energy
density of states.Comment: accepted for publication in J. Phys.
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