1,600 research outputs found
Dynamical Scaling from Multi-Scale Measurements
We present a new measure of the Dynamical Critical behavior: the "Multi-scale
Dynamical Exponent (MDE)"Comment: 9 pages,Latex, Request figures from [email protected]
Ising Model Coupled to Three-Dimensional Quantum Gravity
We have performed Monte Carlo simulations of the Ising model coupled to
three-dimensional quantum gravity based on a summation over dynamical
triangulations. These were done both in the microcanonical ensemble, with the
number of points in the triangulation and the number of Ising spins fixed, and
in the grand canoncal ensemble. We have investigated the two possible cases of
the spins living on the vertices of the triangulation (``diect'' case) and the
spins living in the middle of the tetrahedra (``dual'' case). We observed phase
transitions which are probably second order, and found that the dual
implementation more effectively couples the spins to the quantum gravity.Comment: 11 page
Toward an analytic determination of the deconfinement temperature in SU(2) L.G.T.
We consider the SU(2) lattice gauge theory at finite temperature in (d+1)
dimensions, with different couplings and for timelike and
spacelike plaquettes. By using the character expansion of the Wilson action and
performing the integrals over space-like link variables, we find an effective
action for the Polyakov loops which is exact to all orders in and to
the first non-trivial order in . The critical coupling for the
deconfinement transition is determined in the (3+1) dimensional case, by the
mean field method, for different values of the lattice size in the
compactified time direction and of the asymmetry parameter . We find good agreement with Montecarlo simulations in
the range , and good qualitative agreement in the same range
with the logarithmic scaling law of QCD. Moreover the dependence of the results
from the parameter is in excellent agreement with previous theoretical
predictions.Comment: uuencoded latex file of 32 pages plus 3 ps figure
The Spectrum of the 2+1 Dimensional Gauge Ising Model
We present a high precision Monte Carlo study of the spectrum of the
gauge theory in dimensions in the strong coupling phase. Using state of
the art Monte Carlo techniques we are able to accurately determine up to three
masses in a single channel. We compare our results with the strong coupling
expansion for the lightest mass and with results for the universal ratio
determined for the -theory. Finally the whole spectrum is
compared with that obtained from the Isgur-Paton flux tube model and the
spectrum of the dimensional gauge theory. A remarkable agreement
between the Ising and SU(2) spectra (except for the lowest mass state) is
found.Comment: uuencoded latex file of 22 pages plus 4 ps figure
Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical Staggered Fermions
Complete spectra of the staggered Dirac operator \Dirac are determined in
quenched four-dimensional gauge fields, and also in the presence of
dynamical fermions.
Periodic as well as antiperiodic boundary conditions are used.
An attempt is made to relate the performance of multigrid (MG) and conjugate
gradient (CG) algorithms for propagators with the distribution of the
eigenvalues of~\Dirac.
The convergence of the CG algorithm is determined only by the condition
number~ and by the lattice size.
Since~'s do not vary significantly when quarks become dynamic,
CG convergence in unquenched fields can be predicted from quenched
simulations.
On the other hand, MG convergence is not affected by~ but depends on
the spectrum in a more subtle way.Comment: 19 pages, 8 figures, HUB-IEP-94/12 and KL-TH 19/94; comes as a
uuencoded tar-compressed .ps-fil
Block Spin Effective Action for 4d SU(2) Finite Temperature Lattice Gauge Theory
The Svetitsky-Yaffe conjecture for finite temperature 4d SU(2) lattice gauge
theory is confirmed by observing matching of block spin effective actions of
the gauge model with those of the 3d Ising model. The effective action for the
gauge model is defined by blocking the signs of the Polyakov loops with the
majority rule. To compute it numerically, we apply a variant of the IMCRG
method of Gupta and Cordery.Comment: LaTeX2e, 22 pages, 8 Figure
Screening and Deconfinement of Sources in Finite Temperature SU(2) Lattice Gauge Theory
Deconfinement and screening of higher-representation sources in
finite-temperature lattice gauge theory is investigated by both
analytical and numerical means. The effective Polyakov-line action at strong
coupling is simulated by an efficient cluster-updating Monte Carlo algorithm
for the case of dimensions. The results compare very favourably with
an improved mean-field solution. The limit of the
theory is shown to be highly singular as far as critical behaviour is
concerned. In that limit the leading amplitudes of higher representation
Polyakov lines vanish at strong coupling, and subleading exponents become
dominant. Each of the higher-representation sources then effectively carry with
them their own critical exponents.Comment: 13pages+7figures, CERN-TH-7222/94 One reference added, else unchange
Mean Field Behavior of Cluster Dynamics
The dynamic behavior of cluster algorithms is analyzed in the classical mean
field limit. Rigorous analytical results below establish that the dynamic
exponent has the value for the Swendsen-Wang algorithm and
for the Wolff algorithm.
An efficient Monte Carlo implementation is introduced, adapted for using
these algorithms for fully connected graphs. Extensive simulations both above
and below demonstrate scaling and evaluate the finite-size scaling
function by means of a rather impressive collapse of the data.Comment: Revtex, 9 pages with 7 figure
Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions
We study a multigrid method for nonabelian lattice gauge theory, the time
slice blocking, in two and four dimensions. For SU(2) gauge fields in two
dimensions, critical slowing down is almost completely eliminated by this
method. This result is in accordance with theoretical arguments based on the
analysis of the scale dependence of acceptance rates for nonlocal Metropolis
updates. The generalization of the time slice blocking to SU(2) in four
dimensions is investigated analytically and by numerical simulations. Compared
to two dimensions, the local disorder in the four dimensional gauge field leads
to kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint
MS-TPI-94-
Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity
Computations in Dynamical Triangulation Models of Four-Dimensional Quantum
Gravity involve weighted averaging over sets of all distinct triangulations of
compact four-dimensional manifolds. In order to be able to perform such
computations one needs an algorithm which for any given and a given compact
four-dimensional manifold constructs all possible triangulations of
with simplices. Our first result is that such algorithm does not
exist. Then we discuss recursion-theoretic limitations of any algorithm
designed to perform approximate calculations of sums over all possible
triangulations of a compact four-dimensional manifold.Comment: 8 Pages, LaTex, PUPT-132
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