6,439 research outputs found
Theoretical Analysis of Acceptance Rates in Multigrid Monte Carlo
We analyze the kinematics of multigrid Monte Carlo algorithms by
investigating acceptance rates for nonlocal Metropolis updates. With the help
of a simple criterion we can decide whether or not a multigrid algorithm will
have a chance to overcome critial slowing down for a given model. Our method is
introduced in the context of spin models. A multigrid Monte Carlo procedure for
nonabelian lattice gauge theory is described, and its kinematics is analyzed in
detail.Comment: 7 pages, no figures, (talk at LATTICE 92 in Amsterdam
Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model
Generalized universality, as recently proposed, postulates a universal
non-Gaussian form of the probability density function (PDF) of certain global
observables for a wide class of highly correlated systems of finite volume N.
Studying the 2D XY -model, we link its validity to renormalization group
properties. It would be valid if there were a single dimension 0 operator, but
the actual existence of several such operators leads to T-dependent
corrections. The PDF is the Fourier transform of the partition function Z(q) of
an auxiliary theory which differs by a dimension 0 perturbation with a very
small imaginary coefficient iq/N from a theory which is asymptotically free in
the infrared. We compute the PDF from a systematic loop expansion of ln Z(q).Comment: To be published in Phys. Rev.
Construction of Field Algebras with Quantum Symmetry from Local Observables
It has been discussed earlier that ( weak quasi-) quantum groups allow for
conventional interpretation as internal symmetries in local quantum theory.
From general arguments and explicit examples their consistency with (braid-)
statistics and locality was established. This work addresses to the
reconstruction of quantum symmetries and algebras of field operators. For every
algebra \A of observables satisfying certain standard assumptions, an
appropriate quantum symmetry is found. Field operators are obtained which act
on a positive definite Hilbert space of states and transform covariantly under
the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation
relations, these fields are demonstrated to obey local braid relation.Comment: 50 pages, HUTMP 93-B33
Vortices and confinement at weak coupling
We discuss the physical picture of thick vortices as the mechanism
responsible for confinement at arbitrarily weak coupling in SU(2) gauge theory.
By introducing appropriate variables on the lattice we distinguish between
thin, thick and `hybrid' vortices, the latter involving Z(2) monopole loop
boundaries. We present numerical lattice simulation results that demonstrate
that the full SU(2) string tension at weak coupling arises from the presence of
vortices linked to the Wilson loop. Conversely, excluding linked vortices
eliminates the confining potential. The numerical results are stable under
alternate choice of lattice action as well as a smoothing procedure which
removes short distance fluctuations while preserving long distance physics.Comment: 21 pages, LaTe
Nexus solitons in the center vortex picture of QCD
It is very plausible that confinement in QCD comes from linking of Wilson
loops to finite-thickness vortices with magnetic fluxes corresponding to the
center of the gauge group. The vortices are solitons of a gauge-invariant QCD
action representing the generation of gluon mass. There are a number of other
solitonic states of this action. We discuss here what we call nexus solitons,
in which for gauge group SU(N), up to N vortices meet a a center, or nexus,
provided that the total flux of the vortices adds to zero (mod N). There are
fundamentally two kinds of nexuses: Quasi-Abelian, which can be described as
composites of Abelian imbedded monopoles, whose Dirac strings are cancelled by
the flux condition; and fully non-Abelian, resembling a deformed sphaleron.
Analytic solutions are available for the quasi-Abelian case, and we discuss
variational estimates of the action of the fully non-Abelian nexus solitons in
SU(2). The non-Abelian nexuses carry Chern-Simons number (or topological charge
in four dimensions). Their presence does not change the fundamentals of
confinement in the center-vortex picture, but they may lead to a modified
picture of the QCD vacuum.Comment: LateX, 24 pages, 2 .eps figure
Center vortices and confinement vs. screening
We study adjoint and fundamental Wilson loops in the center-vortex picture of
confinement, for gauge group SU(N) with general N. There are N-1 distinct
vortices, whose properties, including collective coordinates and actions, we
study. In d=2 we construct a center-vortex model by hand so that it has a
smooth large-N limit of fundamental-representation Wilson loops and find, as
expected, confinement. Extending an earlier work by the author, we construct
the adjoint Wilson-loop potential in this d=2 model for all N, as an expansion
in powers of , where is the vortex density per unit area and M
is the vortex inverse size, and find, as expected, screening. The leading term
of the adjoint potential shows a roughly linear regime followed by string
breaking when the potential energy is about 2M. This leading potential is a
universal (N-independent at fixed fundamental string tension ) of the form
, where R is the spacelike dimension of a rectangular Wilson
loop. The linear-regime slope is not necessarily related to by Casimir
scaling. We show that in d=2 the dilute vortex model is essentially equivalent
to true d=2 QCD, but that this is not so for adjoint representations; arguments
to the contrary are based on illegal cumulant expansions which fail to
represent the necessary periodicity of the Wilson loop in the vortex flux. Most
of our arguments are expected to hold in d=3,4 also.Comment: 29 pages, LaTex, 1 figure. Minor changes; references added;
discussion of factorization sharpened. Major conclusions unchange
Effective Field Theories
Effective field theories encode the predictions of a quantum field theory at
low energy. The effective theory has a fairly low ultraviolet cutoff. As a
result, loop corrections are small, at least if the effective action contains a
term which is quadratic in the fields, and physical predictions can be read
straight from the effective Lagrangean.
Methods will be discussed how to compute an effective low energy action from
a given fundamental action, either analytically or numerically, or by a
combination of both methods. Basically,the idea is to integrate out the high
frequency components of fields. This requires the choice of a "blockspin",i.e.
the specification of a low frequency field as a function of the fundamental
fields. These blockspins will be the fields of the effective field theory. The
blockspin need not be a field of the same type as one of the fundamental
fields, and it may be composite. Special features of blockspins in nonabelian
gauge theories will be discussed in some detail.
In analytical work and in multigrid updating schemes one needs interpolation
kernels \A from coarse to fine grid in addition to the averaging kernels
which determines the blockspin. A neural net strategy for finding optimal
kernels is presented.
Numerical methods are applicable to obtain actions of effective theories on
lattices of finite volume. The constraint effective potential) is of particular
interest. In a Higgs model it yields the free energy, considered as a function
of a gauge covariant magnetization. Its shape determines the phase structure of
the theory. Its loop expansion with and without gauge fields can be used to
determine finite size corrections to numerical data.Comment: 45 pages, 9 figs., preprint DESY 92-070 (figs. 3-9 added in ps
format
On Renormalization Group Flows and Polymer Algebras
In this talk methods for a rigorous control of the renormalization group (RG)
flow of field theories are discussed. The RG equations involve the flow of an
infinite number of local partition functions. By the method of exact
beta-function the RG equations are reduced to flow equations of a finite number
of coupling constants. Generating functions of Greens functions are expressed
by polymer activities. Polymer activities are useful for solving the large
volume and large field problem in field theory. The RG flow of the polymer
activities is studied by the introduction of polymer algebras. The definition
of products and recursive functions replaces cluster expansion techniques.
Norms of these products and recursive functions are basic tools and simplify a
RG analysis for field theories. The methods will be discussed at examples of
the -model, the -model and hierarchical scalar field
theory (infrared fixed points).Comment: 32 pages, LaTeX, MS-TPI-94-12, Talk presented at the conference
``Constructive Results in Field Theory, Statistical Mechanics and Condensed
Matter Physics'', 25-27 July 1994, Palaiseau, Franc
Multigrid Monte Carlo with higher cycles in the Sine Gordon model
We study the dynamical critical behavior of multigrid Monte Carlo for the two
dimensional Sine Gordon model on lattices up to 128 x 128. Using piecewise
constant interpolation, we perform a W-cycle (gamma=2). We examine whether one
can reduce critical slowing down caused by decreasing acceptance rates on large
blocks by doing more work on coarser lattices. To this end, we choose a higher
cycle with gamma = 4. The results clearly demonstrate that critical slowing
down is not reduced in either case.Comment: 7 pages, 1 figure, whole paper including figure contained in ps-file,
DESY 93-00
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