36 research outputs found
MEM study of true flattening of free energy and the term
We study the sign problem in lattice field theory with a term, which
reveals as flattening phenomenon of the free energy density . We
report the result of the MEM analysis, where such mock data are used that
`true' flattening of occurs. This is regarded as a simple model for
studying whether the MEM could correctly detect non trivial phase structure in
space. We discuss how the MEM distinguishes fictitious and true
flattening.Comment: Poster presented at Lattice2004(topology), Fermilab, June 21-26,
2004; 3 pages, 3 figure
Lattice Field Theory with the Sign Problem and the Maximum Entropy Method
Although numerical simulation in lattice field theory is one of the most
effective tools to study non-perturbative properties of field theories, it
faces serious obstacles coming from the sign problem in some theories such as
finite density QCD and lattice field theory with the term. We
reconsider this problem from the point of view of the maximum entropy method.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Maximum Entropy Method Approach to Term
In Monte Carlo simulations of lattice field theory with a term, one
confronts the complex weight problem, or the sign problem. This is circumvented
by performing the Fourier transform of the topological charge distribution
. This procedure, however, causes flattening phenomenon of the free
energy , which makes study of the phase structure unfeasible.
In order to treat this problem, we apply the maximum entropy method (MEM) to
a Gaussian form of , which serves as a good example to test whether the
MEM can be applied effectively to the term. We study the case with
flattening as well as that without flattening. In the latter case, the results
of the MEM agree with those obtained from the direct application of the Fourier
transform. For the former, the MEM gives a smoother than that of
the Fourier transform. Among various default models investigated, the images
which yield the least error do not show flattening, although some others cannot
be excluded given the uncertainty related to statistical error.Comment: PTPTEX , 25 pages with 11 figure
Two dimensional CP^2 Model with \theta-term and Topological Charge Distributions
Topological charge distributions in 2 dimensional CP^2 model with theta-term
is calculated. In strong coupling regions, topological charge distribution is
approximately given by Gaussian form as a function of topological charge and
this behavior leads to the first order phase transition at \theta=\pi. In weak
coupling regions it shows non-Gaussian distribution and the first order phase
transition disappears. Free energy as a function of \theta shows "flattening"
behavior at theta=theta_f<pi, when we calculate the free energy directly from
topological charge distribution. Possible origin of this flattening phenomena
is prensented.Comment: 17 pages,7 figure
CP model with the theta term and maximum entropy method
A term in lattice field theory causes the sign problem in Monte
Carlo simulations. This problem can be circumvented by Fourier-transforming the
topological charge distribution . This strategy, however, has a
limitation, because errors of prevent one from calculating the partition
function
properly for large volumes. This is called flattening. As
an alternative approach to the Fourier method, we utilize the maximum entropy
method (MEM) to calculate . We apply the MEM to Monte Carlo
data of the CP model. It is found that in the non-flattening case, the
result of the MEM agrees with that of the Fourier transform, while in the
flattening case, the MEM gives smooth
.Comment: Talk presented at Lattice2004(topology), Fermilab, June 21-26, 2004;
3 pages, 3 figure
Application of Maximum Entropy Method to Lattice Field Theory with a Topological Term
In Monte Carlo simulation, lattice field theory with a term suffers
from the sign problem.
This problem can be circumvented by Fourier-transforming the topological
charge distribution . Although this strategy works well for small lattice
volume, effect of errors of
becomes serious with increasing volume and prevents one from studying
the phase structure. This is called flattening. As an alternative approach, we
apply the maximum entropy method (MEM) to the Gaussian . It is found that
the flattening could be much improved by use of the MEM.Comment: talk at Lattice 2003 (topology), 3 pages with 3 figure
Sign problem and MEM in lattice field theory with the term
Lattice field theory with the term suffers from the sign problem.
The sign problem appears as flattening of the free energy.
As an alternative to the conventional method, the Fourier transform method
(FTM), we apply the maximum entropy method (MEM) to Monte Carlo data obtained
using the CP model with the term.
For data without flattening, we obtain the most probable images of the
partition function with rather small errors. The
results are quantitatively close to the result obtained with the
FTM. Motivated by this fact, we systematically investigate flattening in
terms of the MEM.
Obtained images are consistent with the FTM for
small values of , while the behavior of
depends strongly on the default model for large values of .
This behavior of reflects the flattening phenomenon.Comment: PTPTEX, 20 pages with 15 figure
String Junction Model, Cluster Hypothesis, Penta-Quark Baryon and Tetra-Quark Meson
Thirty years ago we proposed string junction model of hadrons and examined
structure and reaction of hadrons including exotic ones. Mass of exotic
hadrons of light quarks is roughly given by , where
is the total number of junctions and GeV is the ordinary light
baryon mass. In this paper we introduce "cluster hypothesis" into the model by
which mass of a complex hadron is given by the sum of masses of clusters
composing it. The hypothesis guarantees the established picture that mass
differences of hadrons of the same string junction structure are due to those
of the constituent quarks. A candidate for penta-quark baryon (1530
MeV, including a strange anti-quark {\sb} and that for tetra-quark
meson (4430 MeV) recently reported by the Bell collaboration are examined
in parallel. is considered to have non-strange partners, which are
lighter by the mass difference between strange and non-strange
quarks. Mass of such light penta-quark baryons with is expected to be
about 3 GeV. Several parameters of the model are estimated such as mass of
junction of MeV. While mass of light tetra-quark meson with
is expected to be about 2 GeV, (4430 MeV) containing
(u,c,{\db},{\cb}) gives a clue to determine some parameters of the model,
e.g., inter-junction string energy .Comment: 17 pages, 4 figures, correction is made, extensively revise