45,270 research outputs found
Biased Metropolis-Heat-Bath Algorithm for Fundamental-Adjoint SU(2) Lattice Gauge Theory
For SU(2) lattice gauge theory with the fundamental-adjoint action an
efficient heat-bath algorithm is not known so that one had to rely on
Metropolis simulations supplemented by overrelaxation. Implementing a novel
biased Metropolis-heat-bath algorithm for this model, we find improvement
factors in the range 1.45 to 2.06 over conventionally optimized Metropolis
simulations. If one optimizes further with respect to additional overrelaxation
sweeps, the improvement factors are found in the range 1.3 to 1.8.Comment: 4 pages, 2 figures; minor changes and one reference added; accepted
for publication in PR
Non-Extensive Bose-Einstein Condensation Model
The imperfect Boson gas supplemented with a gentle repulsive interaction is
completely solved. In particular it is proved that it has non-extensive
Bose-Einstein condensation, i.e., there is condensation without macroscopic
occupation of the ground state (k=0) level
Exchange Monte Carlo Method and Application to Spin Glass Simulations
We propose an efficient Monte Carlo algorithm for simulating a
``hardly-relaxing" system, in which many replicas with different temperatures
are simultaneously simulated and a virtual process exchanging configurations of
these replica is introduced. This exchange process is expected to let the
system at low temperatures escape from a local minimum. By using this algorithm
the three-dimensional Ising spin glass model is studied. The ergodicity
time in this method is found much smaller than that of the multi-canonical
method. In particular the time correlation function almost follows an
exponential decay whose relaxation time is comparable to the ergodicity time at
low temperatures. It suggests that the system relaxes very rapidly through the
exchange process even in the low temperature phase.Comment: 10 pages + uuencoded 5 Postscript figures, REVTe
Multicanonical Recursions
The problem of calculating multicanonical parameters recursively is
discussed. I describe in detail a computational implementation which has worked
reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded
Z-compressed .tar file created by uufiles), figure file corrected
Vector boson mass generation without new fields
Previously a model of only vector fields with a local U(2) symmetry was
introduced for which one finds a massless U(1) photon and a massive SU(2)
vector boson in the lattice regularization. Here it is shown that quantization
of its classical continuum action leads to perturbative renormalization
difficulties. But, non-perturbative Monte Carlo calculations favor the
existence of a quantum continuum limit.Comment: 4 pages, 3 figures, 2 tables. Revised after referee reports. One
error eliminate
Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity
We present some open problems and obtain some partial results for spectral
optimization problems involving measure, torsional rigidity and first Dirichlet
eigenvalue.Comment: 18 pages, 4 figure
Density of states and Fisher's zeros in compact U(1) pure gauge theory
We present high-accuracy calculations of the density of states using
multicanonical methods for lattice gauge theory with a compact gauge group U(1)
on 4^4, 6^4 and 8^4 lattices. We show that the results are consistent with weak
and strong coupling expansions. We present methods based on Chebyshev
interpolations and Cauchy theorem to find the (Fisher's) zeros of the partition
function in the complex beta=1/g^2 plane. The results are consistent with
reweighting methods whenever the latter are accurate. We discuss the volume
dependence of the imaginary part of the Fisher's zeros, the width and depth of
the plaquette distribution at the value of beta where the two peaks have equal
height. We discuss strategies to discriminate between first and second order
transitions and explore them with data at larger volume but lower statistics.
Higher statistics and even larger lattices are necessary to draw strong
conclusions regarding the order of the transition.Comment: 14 pages, 16 figure
Overlap Distribution of the Three-Dimensional Ising Model
We study the Parisi overlap probability density P_L(q) for the
three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations.
At the critical point P_L(q) is peaked around q=0 in contrast with the double
peaked magnetic probability density. We give particular attention to the tails
of the overlap distribution at the critical point, which we control over up to
500 orders of magnitude by using the multi-overlap MC algorithm. Below the
critical temperature interface tension estimates from the overlap probability
density are given and their approach to the infinite volume limit appears to be
smoother than for estimates from the magnetization.Comment: 7 pages, RevTex, 9 Postscript figure
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