993 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
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
Complex wave function, Chiral spin order parameter and Phase Problem
We study the two dimensional Hubbard model by use of the ground state
algorithm in the Monte Carlo simulation. We employ complex wave functions as
trial function in order to have a close look at properties such as chiral spin
order (SO) and flux phase. For half filling, a particle-hole
transformation leads to sum rules with respect to the Green's functions for a
certain choice of a set of wave functions. It is then analytically shown that
the sum rules lead to the absence of the SO. Upon doping, we are
confronted with the sign problem, which in our case %ch appears as a ``phase
problem" due to the phase of the Monte Carlo weights. The average of the phase
shows an exponential decay as a function of inverse temperature similarly to
that of sign by Loh Jr. et. al. . We compare the numerical results with those
of exact numerical calculations.Comment: 28 pages, 9 figures(hard copy will be available upon request
Tetraquarks and Pentaquarks in String Models
We consider the production and decay of multiquark systems in the framework
of string models where the hadron structure is determined by valence quarks
together with string junctions. We show that the low mass multiquark resonances
can be very narrow.Comment: 7 pages, 2 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
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
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