1,025 research outputs found
Dimensional reduction and a Z(3) symmetric model
We present first results from a numerical investigation of a Z(3) symmetric
model based on dimensional reduction.Comment: Talk presented at XXI International Symposium on Lattice Field Theory
lattice2003(Non-zero temperature and density
Ensemble of causal trees
We discuss the geometry of trees endowed with a causal structure using the
conventional framework of equilibrium statistical mechanics. We show how this
ensemble is related to popular growing network models. In particular we
demonstrate that on a class of afine attachment kernels the two models are
identical but they can differ substantially for other choice of weights. We
show that causal trees exhibit condensation even for asymptotically linear
kernels. We derive general formulae describing the degree distribution, the
ancestor-descendant correlation and the probability a randomly chosen node
lives at a given geodesic distance from the root. It is shown that the
Hausdorff dimension d_H of the causal networks is generically infinite.Comment: 11 Pages, published in proceedings of Random Geometry Workshop May
15-17, 2003 Krako
Screening Masses in Dimensionally Reduced (2+1)D Gauge Theory
We discuss the screening masses and residue factorisation of the SU(3) (2+1)D
theory in the dimensional reduction formalism. The phase structure of the
reduced model is also investigated.Comment: 3 pages, Lattice 2001(gaugetheories
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
Collapse of 4D random geometries
We extend the analysis of the Backgammon model to an ensemble with a fixed
number of balls and a fluctuating number of boxes. In this ensemble the model
exhibits a first order phase transition analogous to the one in higher
dimensional simplicial gravity. The transition relies on a kinematic
condensation and reflects a crisis of the integration measure which is probably
a part of the more general problem with the measure for functional integration
over higher (d>2) dimensional Riemannian structures.Comment: 7 pages, Latex2e, 2 figures (.eps
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
The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs
We study with Monte Carlo methods an ensemble of c=-5 gravity graphs,
generated by coupling a conformal field theory with central charge c=-5 to
two-dimensional quantum gravity. We measure the fractal properties of the
ensemble, such as the string susceptibility exponent gamma_s and the intrinsic
fractal dimensions d_H. We find gamma_s = -1.5(1) and d_H = 3.36(4), in
reasonable agreement with theoretical predictions. In addition, we study the
critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs
and show that it agrees, within numerical accuracy, with theoretical
predictions for the critical behavior of an Ising model coupled dynamically to
two-dimensional quantum gravity, provided the total central charge of the
matter sector is c=-5. From this we conjecture that the critical behavior of
the Ising model is determined solely by the average fractal properties of the
graphs, the coupling to the geometry not playing an important role.Comment: 23 pages, Latex, 7 figure
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
Phase diagram of the mean field model of simplicial gravity
We discuss the phase diagram of the balls in boxes model, with a varying
number of boxes. The model can be regarded as a mean-field model of simplicial
gravity. We analyse in detail the case of weights of the form , which correspond to the measure term introduced in the simplicial
quantum gravity simulations. The system has two phases~: {\em elongated} ({\em
fluid}) and {\em crumpled}. For the transition between
these two phases is first order, while for it is continuous.
The transition becomes softer when approaches unity and eventually
disappears at . We then generalise the discussion to an arbitrary set
of weights. Finally, we show that if one introduces an additional kinematic
bound on the average density of balls per box then a new {\em condensed} phase
appears in the phase diagram. It bears some similarity to the {\em crinkled}
phase of simplicial gravity discussed recently in models of gravity interacting
with matter fields.Comment: 15 pages, 5 figure
Dimensional reduction in QCD: Lessons from lower dimensions
In this contribution we present the results of a series of investigations of
dimensional reduction, applied to SU(3) gauge theory in 2 + 1 dimensions. We
review earlier results, present a new reduced model with Z(3) symmetry, and
discuss the results of numerical simulations of this model.Comment: 10 pages, Talk given at Workshop on Finite Density QCD, Nara Japan
10-12 Jul 200
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