2,838 research outputs found
Universality class for bootstrap percolation with on the cubic lattice
We study the bootstrap percolation model on a cubic lattice, using
Monte Carlo simulation and finite-size scaling techniques. In bootstrap
percolation, sites on a lattice are considered occupied (present) or vacant
(absent) with probability or , respectively. Occupied sites with less
than occupied first-neighbours are then rendered unoccupied; this culling
process is repeated until a stable configuration is reached. We evaluate the
percolation critical probability, , and both scaling powers, and
, and, contrarily to previous calculations, our results indicate that the
model belongs to the same universality class as usual percolation (i.e.,
). The critical spanning probability, , is also numerically
studied, for systems with linear sizes ranging from L=32 up to L=480: the value
we found, , is the same as for usual percolation with
free boundary conditions.Comment: 11 pages; 4 figures; to appear in Int. J. Mod. Phys.
Phase structure of lattice QCD at finite temperature for 2+1 flavors of Kogut-Susskind quarks
We report on a study of the finite-temperature chiral transition on an
lattice for 2+1 flavors of Kogut-Susskind quarks. We find the point of
physical quark masses to lie in the region of crossover, in agreement with
results of previous studies. Results of a detailed examination of the
case indicate vanishing of the screening mass of meson
at the end point of the first-order transition.Comment: LATTICE98(hightemp), 3 pages, 4 figure
The Phase Diagram of Compact QED Coupled to a Four-Fermi Interaction
Compact lattice Quantum Electrodynamics (QED) with four species of fermions
is simulated with massless quarks by using the QED scheme of adding a
four-fermi interaction to the action. Simulations directly in the chiral limit
of massless quarks are done with high statistics on , and lattices,
and the phase diagram, parameterized by the gauge and the four-fermi couplings,
is mapped out. The line of monopole condensation transitions is separate from
the line of chiral symmetry restoration. The simulation results indicate that
the monopole condensation transition is first order while the chiral transition
is second order. The challenges in determining the Universality class of the
chiral transition are discussed. If the scaling region for the chiral
transition is sufficiently wide, the simulations predict critical
indices far from mean field values. We discuss a speculative scenario in which
anti-screening provided by double-helix strands of monopole and anti-monopole
loops are the agent that balances the screening of fermion anti-fermion pairs
to produce an ultra-violet fixed point in the electric coupling.Comment: 29 pages, 8 figures and 2 table
Anomaly and a QCD-like phase diagram with massive bosonic baryons
We study a strongly coupled lattice gauge theory with two flavors of
quarks, invariant under an exact symmetry which is the same as QCD with
two flavors of quarks without an anomaly. The model also contains a coupling
that can be used to break the symmetry and thus mimic the QCD
anomaly. At low temperatures and small baryon chemical potential
the model contains massless pions and massive bosonic baryons similar to QCD
with an even number of colors. In this work we study the phase
diagram of the model and show that it contains three phases : (1) A chirally
broken phase at low and , (2) a chirally symmetric baryon superfluid
phase at low and high , and (3) a symmetric phase at high . We
find that the nature of the finite temperature chiral phase transition and in
particular the location of the tricritical point that seperates the first order
line from the second order line is affected significantly by the anomaly.Comment: 22 pages, 16 figures, 5 tables, references adde
Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB Anisotropy
We use simulated maps of the cosmic microwave background anisotropy to
quantify the ability of different statistical tests to discriminate between
Gaussian and non-Gaussian models. Despite the central limit theorem on large
angular scales, both the genus and extrema correlation are able to discriminate
between Gaussian models and a semi-analytic texture model selected as a
physically motivated non-Gaussian model. When run on the COBE 4-year CMB maps,
both tests prefer the Gaussian model. Although the bispectrum has comparable
statistical power when computed on the full sky, once a Galactic cut is imposed
on the data the bispectrum loses the ability to discriminate between models.
Off-diagonal elements of the bispectrum are comparable to the diagonal elements
for the non-Gaussian texture model and must be included to obtain maximum
statistical power.Comment: Accepted for publication in ApJ; 20 pages, 6 figures, uses AASTeX
v5.
Phase structure of lattice QCD for general number of flavors
We investigate the phase structure of lattice QCD for the general number of
flavors in the parameter space of gauge coupling constant and quark mass,
employing the one-plaquette gauge action and the standard Wilson quark action.
Performing a series of simulations for the number of flavors --360 with
degenerate-mass quarks, we find that when there is a line of a bulk
first order phase transition between the confined phase and a deconfined phase
at a finite current quark mass in the strong coupling region and the
intermediate coupling region. The massless quark line exists only in the
deconfined phase. Based on these numerical results in the strong coupling limit
and in the intermediate coupling region, we propose the following phase
structure, depending on the number of flavors whose masses are less than
which is the physical scale characterizing the phase transition in
the weak coupling region: When , there is only a trivial IR fixed
point and therefore the theory in the continuum limit is free. On the other
hand, when , there is a non-trivial IR fixed point and
therefore the theory is non-trivial with anomalous dimensions, however, without
quark confinement. Theories which satisfy both quark confinement and
spontaneous chiral symmetry breaking in the continuum limit exist only for .Comment: RevTeX, 20 pages, 43 PS figure
Pathologies of Quenched Lattice QCD at non--zero Density and its Effective Potential
We simulate lattice QCD at non--zero baryon density and zero temperature in
the quenched approximation, both in the scaling region and in the infinite
coupling limit. We investigate the nature of the forbidden region -- the range
of chemical potential where the simulations grow prohibitively expensive, and
the results, when available, are puzzling if not unphysical. At weak coupling
we have explored the sensitivity of these pathologies to the lattice size, and
found that using a large lattice () does not remove them. The
effective potential sheds considerable light on the problems in the
simulations, and gives a clear interpretation of the forbidden region. The
strong coupling simulations were particularly illuminating on this point.Comment: 49 pages, uu-encoded expanding to postscript;also available at
ftp://hlrz36.hlrz.kfa-juelich.de/pub/mpl/hlrz72_95.p
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