1,263 research outputs found
Lattice study of the simplified model of M-theory for larger gauge groups
Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is
dis cussed. First results of the quenched Monte Carlo simulations, for D=4 and
with higher g auge groups (3 <= N <= 8), are presented. We confirm an earlier
(N=2) evidence tha t the system reveals different behaviours at low and high
temperatures separated by a narrow transiti on region. These two regimes may
correspond to a black hole and elementary excitations phases conjectured in the
M-theory. Dependence of the "transition temperature" on N is consistent with 't
Hooft scaling and shows a smooth saturation of lattice results towards the
large N limit. Is not yet resolved if the observed change between the two
regimes corresponds to a genuine phase transition or to a gentle crossover . A
new, noncompact formulation of the lattice model is also proposed and its
advantages are briefly discussed.Comment: 10 pages, 2 figures, Invited talk presented at the Sixth Workshop on
Non-Perturbative QCD, American University of Paris, Paris, June, 200
Measuring an entropy in heavy ion collisions
We propose to use the coincidence method of Ma to measure an entropy of the
system created in heavy ion collisions. Moreover we estimate, in a simple
model, the values of parameters for which the thermodynamical behaviour sets
in.Comment: LATTICE98(hightemp), 3 pages, LaTeX with two eps figure
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
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
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
Replica analysis of a preferential urn model
We analyse a preferential urn model with randomness using the replica method.
The preferential urn model is a stochastic model based on the concept "the rich
get richer." The replica analysis clarifies that the preferential urn model
with randomness shows a fat-tailed occupation distribution. The analytical
treatments and results would be useful for various research fields such as
complex networks, stochastic models, and econophysics.Comment: 6 pages, 2 figure
Exotic trees
We discuss the scaling properties of free branched polymers. The scaling
behaviour of the model is classified by the Hausdorff dimensions for the
internal geometry: d_L and d_H, and for the external one: D_L and D_H. The
dimensions d_H and D_H characterize the behaviour for long distances while d_L
and D_L for short distances. We show that the internal Hausdorff dimension is
d_L=2 for generic and scale-free trees, contrary to d_H which is known be equal
two for generic trees and to vary between two and infinity for scale-free
trees. We show that the external Hausdorff dimension D_H is directly related to
the internal one as D_H = \alpha d_H, where \alpha is the stability index of
the embedding weights for the nearest-vertex interactions. The index is
\alpha=2 for weights from the gaussian domain of attraction and 0<\alpha <2 for
those from the L\'evy domain of attraction. If the dimension D of the target
space is larger than D_H one finds D_L=D_H, or otherwise D_L=D. The latter
result means that the fractal structure cannot develop in a target space which
has too low dimension.Comment: 33 pages, 6 eps figure
Density correlators in a self-similar cascade
Multivariate density moments (correlators) of arbitrary order are obtained
for the multiplicative self-similar cascade. This result is based on the
calculation by Greiner, Eggers and Lipa (reference [1]) where the correlators
of the logarithms of the particle densities have been obtained. The density
correlators, more suitable for comparison with multiparticle data, appear to
have even simpler form than those obtained in [1].Comment: 9 pages, 3 figures, uses epsfig.st
Condensation in nongeneric trees
We study nongeneric planar trees and prove the existence of a Gibbs measure
on infinite trees obtained as a weak limit of the finite volume measures. It is
shown that in the infinite volume limit there arises exactly one vertex of
infinite degree and the rest of the tree is distributed like a subcritical
Galton-Watson tree with mean offspring probability . We calculate the rate
of divergence of the degree of the highest order vertex of finite trees in the
thermodynamic limit and show it goes like where is the size of the
tree. These trees have infinite spectral dimension with probability one but the
spectral dimension calculated from the ensemble average of the generating
function for return probabilities is given by if the weight
of a vertex of degree is asymptotic to .Comment: 57 pages, 14 figures. Minor change
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