507 research outputs found
Correlation functions and critical behaviour on fluctuating geometries
We study the two-point correlation function in the model of branched polymers
and its relation to the critical behaviour of the model. We show that the
correlation function has a universal scaling form in the generic phase with the
only scale given by the size of the polymer. We show that the origin of the
singularity of the free energy at the critical point is different from that in
the standard statistical models. The transition is related to the change of the
dimensionality of the system.Comment: 10 Pages, Latex2e, uses elsart.cls, 1 figure include
Connected Correlators in Quantum Gravity
We discuss the concept of connected, reparameterization invariant matter
correlators in quantum gravity. We analyze the effect of discretization in two
solvable cases: branched polymers and two-dimensional simplicial gravity. In
both cases the naively defined connected correlators for a fixed volume display
an anomalous behavior, which could be interpreted as a long-range order. We
suggest that this is in fact only a highly non-trivial finite-size effect and
propose an improved definition of the connected correlator, which reduces the
effect. Using this definition we illustrate the appearance of a long-range spin
order in the Ising model on a two-dimensional random lattice in an external
magnetic field , when and .Comment: 21 pages, 8 figure
Connected Correlators in Random Geometries
We analyze correlation functions in a toy model of a random geometry interacting with matter. We show that in general the connected correlator will contain a long-range scaling part which is in some sense a remnant of the disconnected part. This result supports the previously conjectured general form of correlation functions. We discuss the interplay between matter and geometry and the role of the symmetry in the matter sector
RG flow in an exactly solvable model with fluctuating geometry
A recently proposed renormalization group technique, based on the
hierarchical structures present in theories with fluctuating geometry, is
implemented in the model of branched polymers. The renormalization group
equations can be solved analytically, and the flow in coupling constant space
can be determined.Comment: References updated, typos corrected and abstract sligtly changed. 10
pages. Pictex use
Signal from noise retrieval from one and two-point Green's function - comparison
We compare two methods of eigen-inference from large sets of data, based on
the analysis of one-point and two-point Green's functions, respectively. Our
analysis points at the superiority of eigen-inference based on one-point
Green's function. First, the applied by us method based on Pad?e approximants
is orders of magnitude faster comparing to the eigen-inference based on
uctuations (two-point Green's functions). Second, we have identified the source
of potential instability of the two-point Green's function method, as arising
from the spurious zero and negative modes of the estimator for a variance
operator of the certain multidimensional Gaussian distribution, inherent for
the two-point Green's function eigen-inference method. Third, we have presented
the cases of eigen-inference based on negative spectral moments, for strictly
positive spectra. Finally, we have compared the cases of eigen-inference of
real-valued and complex-valued correlated Wishart distributions, reinforcing
our conclusions on an advantage of the one-point Green's function method.Comment: 14 pages, 8 figures, 3 table
Order parameters in spin-spin and plaquette lattice theories
We present some basic properties of the gauge theories in the lattice formulation. We discuss the possible order parameters of the theory and their usefulness from the point of view of the numerical calculations. We study the properties of the low coupling constant expansion, i.e. the continuum limit of the theory. Finally we show the results of the numerical calculations for various lattice systems
Search for Scaling Dimensions for Random Surfaces with c=1
We study numerically the fractal structure of the intrinsic geometry of
random surfaces coupled to matter fields with . Using baby universe
surgery it was possible to simulate randomly triangulated surfaces made of
260.000 triangles. Our results are consistent with the theoretical prediction
for the intrinsic Hausdorff dimension.Comment: 10 pages, (csh will uudecode and uncompress ps-file), NBI-HE-94-3
Wealth Condensation in Pareto Macro-Economies
We discuss a Pareto macro-economy (a) in a closed system with fixed total
wealth and (b) in an open system with average mean wealth and compare our
results to a similar analysis in a super-open system (c) with unbounded wealth.
Wealth condensation takes place in the social phase for closed and open
economies, while it occurs in the liberal phase for super-open economies. In
the first two cases, the condensation is related to a mechanism known from the
balls-in-boxes model, while in the last case to the non-integrable tails of the
Pareto distribution. For a closed macro-economy in the social phase, we point
to the emergence of a ``corruption'' phenomenon: a sizeable fraction of the
total wealth is always amassed by a single individual.Comment: 4 pages, 1 figur
The moduli space of isometry classes of globally hyperbolic spacetimes
This is the last article in a series of three initiated by the second author.
We elaborate on the concepts and theorems constructed in the previous articles.
In particular, we prove that the GH and the GGH uniformities previously
introduced on the moduli space of isometry classes of globally hyperbolic
spacetimes are different, but the Cauchy sequences which give rise to
well-defined limit spaces coincide. We then examine properties of the strong
metric introduced earlier on each spacetime, and answer some questions
concerning causality of limit spaces. Progress is made towards a general
definition of causality, and it is proven that the GGH limit of a Cauchy
sequence of , path metric Lorentz spaces is again a
, path metric Lorentz space. Finally, we give a
necessary and sufficient condition, similar to the one of Gromov for the
Riemannian case, for a class of Lorentz spaces to be precompact.Comment: 29 pages, 9 figures, submitted to Class. Quant. Gra
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