95 research outputs found
Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning
We show that linear congruential pseudo-random-number generators can cause
systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm,
if the lattice size is a multiple of a very large power of 2 and one random
number is used per bond. These systematic errors arise from correlations within
a single bond-update half-sweep. The errors can be eliminated (or at least
radically reduced) by updating the bonds in a random order or in an aperiodic
manner. It also helps to use a generator of large modulus (e.g. 60 or more
bits).Comment: Revtex4, 4 page
Curved geometry and Graphs
Quantum Graphity is an approach to quantum gravity based on a background
independent formulation of condensed matter systems on graphs. We summarize
recent results obtained on the notion of emergent geometry from the point of
view of a particle hopping on the graph. We discuss the role of connectivity in
emergent Lorentzian perturbations in a curved background and the Bose--Hubbard
(BH) model defined on graphs with particular symmetries.Comment: are welcome. 4pp, 2 fig. Proceedings of Loops'11 Conference, Madri
Stability analysis of coupled map lattices at locally unstable fixed points
Numerical simulations of coupled map lattices (CMLs) and other complex model
systems show an enormous phenomenological variety that is difficult to classify
and understand. It is therefore desirable to establish analytical tools for
exploring fundamental features of CMLs, such as their stability properties.
Since CMLs can be considered as graphs, we apply methods of spectral graph
theory to analyze their stability at locally unstable fixed points for
different updating rules, different coupling scenarios, and different types of
neighborhoods. Numerical studies are found to be in excellent agreement with
our theoretical results.Comment: 22 pages, 6 figures, accepted for publication in European Physical
Journal
Quantum Field Theory on the Noncommutative Plane with Symmetry
We study properties of a scalar quantum field theory on the two-dimensional
noncommutative plane with quantum symmetry. We start from the
consideration of a firstly quantized quantum particle on the noncommutative
plane. Then we define quantum fields depending on noncommutative coordinates
and construct a field theoretical action using the -invariant measure
on the noncommutative plane. With the help of the partial wave decomposition we
show that this quantum field theory can be considered as a second quantization
of the particle theory on the noncommutative plane and that this field theory
has (contrary to the common belief) even more severe ultraviolet divergences
than its counterpart on the usual commutative plane. Finally, we introduce the
symmetry transformations of physical states on noncommutative spaces and
discuss them in detail for the case of the quantum group.Comment: LaTeX, 26 page
Non-commutative Oscillators and the commutative limit
It is shown in first order perturbation theory that anharmonic oscillators in
non-commutative space behave smoothly in the commutative limit just as harmonic
oscillators do. The non-commutativity provides a method for converting a
problem in degenerate perturbation theory to a non-degenerate problem.Comment: Latex, 6 pages, Minor changes and references adde
The Energy-Momentum Tensor in Noncommutative Gauge Field Models
We discuss the different possibilities of constructing the various
energy-momentum tensors for noncommutative gauge field models. We use Jackiw's
method in order to get symmetric and gauge invariant stress tensors--at least
for commutative gauge field theories. The noncommutative counterparts are
analyzed with the same methods. The issues for the noncommutative cases are
worked out.Comment: 11 pages, completed reference
Parametric Representation of Noncommutative Field Theory
In this paper we investigate the Schwinger parametric representation for the
Feynman amplitudes of the recently discovered renormalizable quantum
field theory on the Moyal non commutative space. This
representation involves new {\it hyperbolic} polynomials which are the
non-commutative analogs of the usual "Kirchoff" or "Symanzik" polynomials of
commutative field theory, but contain richer topological information.Comment: 31 pages,10 figure
Perturbation theory of the space-time non-commutative real scalar field theories
The perturbative framework of the space-time non-commutative real scalar
field theory is formulated, based on the unitary S-matrix. Unitarity of the
S-matrix is explicitly checked order by order using the Heisenberg picture of
Lagrangian formalism of the second quantized operators, with the emphasis of
the so-called minimal realization of the time-ordering step function and of the
importance of the -time ordering. The Feynman rule is established and is
presented using scalar field theory. It is shown that the divergence
structure of space-time non-commutative theory is the same as the one of
space-space non-commutative theory, while there is no UV-IR mixing problem in
this space-time non-commutative theory.Comment: Latex 26 pages, notations modified, add reference
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