24 research outputs found
Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory
We analyze Regge quantum gravity coupled to SU(2) gauge theory on , and simplicial lattices. It turns out that
the window of the well-defined phase of the gravity sector where geometrical
expectation values are stable extends to negative gravitational couplings as
well as to gauge couplings across the deconfinement phase transition. We study
the string tension from Polyakov loops, compare with the -function of
pure gauge theory and conclude that a physical limit through scaling is
possible.Comment: RevTeX, 14 pages, 5 figures (2 eps, 3 tex), 2 table
Phase diagram of d=4 Ising Model with two couplings
We study the phase diagram of the four dimensional Ising model with first and
second neighbour couplings, specially in the antiferromagnetic region, by using
Mean Field and Monte Carlo methods. From the later, all the transition lines
seem to be first order except that between ferromagnetic and disordered phases
in a region including the first-neighbour Ising transition point.Comment: Latex file and 4 figures (epsfig required). It replaces the preprint
entitled "Non-classical exponents in the d=4 Ising Model with two couplings".
New analysis with more statistical data is performed. Final version to appear
in Phys. Lett.
Finite-time fluctuations in the degree statistics of growing networks
This paper presents a comprehensive analysis of the degree statistics in
models for growing networks where new nodes enter one at a time and attach to
one earlier node according to a stochastic rule. The models with uniform
attachment, linear attachment (the Barab\'asi-Albert model), and generalized
preferential attachment with initial attractiveness are successively
considered. The main emphasis is on finite-size (i.e., finite-time) effects,
which are shown to exhibit different behaviors in three regimes of the
size-degree plane: stationary, finite-size scaling, large deviations.Comment: 33 pages, 7 figures, 1 tabl
Mean-field analysis of the q-voter model on networks
We present a detailed investigation of the behavior of the nonlinear q-voter
model for opinion dynamics. At the mean-field level we derive analytically, for
any value of the number q of agents involved in the elementary update, the
phase diagram, the exit probability and the consensus time at the transition
point. The mean-field formalism is extended to the case that the interaction
pattern is given by generic heterogeneous networks. We finally discuss the case
of random regular networks and compare analytical results with simulations.Comment: 20 pages, 10 figure
The Harris-Luck criterion for random lattices
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly diluted
sites or a quasi-periodicity of the lattice, for altering the critical behavior
of a coupled matter system. We investigate the applicability of this type of
criterion to the case of spin variables coupled to random lattices. Their
aptitude to alter critical behavior depends on the degree of spatial
correlations present, which is quantified by a wandering exponent. We consider
the cases of Poissonian random graphs resulting from the Voronoi-Delaunay
construction and of planar, ``fat'' Feynman diagrams and precisely
determine their wandering exponents. The resulting predictions are compared to
various exact and numerical results for the Potts model coupled to these
quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one
figure added for clarification, minor re-wordings and typo cleanu
Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes
We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces
Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
We discuss how to extract renormalized from bare Polyakov loops in SU(N)
lattice gauge theories at nonzero temperature in four spacetime dimensions.
Single loops in an irreducible representation are multiplicatively renormalized
without mixing, through a renormalization constant which depends upon both
representation and temperature. The values of renormalized loops in the four
lowest representations of SU(3) were measured numerically on small, coarse
lattices. We find that in magnitude, condensates for the sextet and octet loops
are approximately the square of the triplet loop. This agrees with a large
expansion, where factorization implies that the expectation values of loops in
adjoint and higher representations are just powers of fundamental and
anti-fundamental loops. For three colors, numerically the corrections to the
large relations are greatest for the sextet loop, ; these
represent corrections of for N=3. The values of the renormalized
triplet loop can be described by an SU(3) matrix model, with an effective
action dominated by the triplet loop. In several ways, the deconfining phase
transition for N=3 appears to be like that in the matrix model of
Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion
for clarity, results unchange
The step free-energy and the behaviour at the roughening transition of lattice gauge theories
The step free-energy is the cost in free energy to create a single step in a planar Wilson loop. We compute it, per unit length, to eighth order in a strong coupling expansion of 3-D and 4-D Z2 gauge theories, and analyse its vanishing at the roughening transition. Our results are consistent with an essential singularity exp — C(tR - t)-1/2, expected from a relationship with the XY-model.L'énergie libre de marche est le coût nécessaire à la création d'une marche sur une boucle de Wilson plate. Nous avons calculé cette quantité par unité de longueur au 8e ordre dans le développement de couplage fort des théories de jauge Z2 sur réseau à 3 et 4 dimensions. Nous avons analysé la façon dont elle s'annule à la transition rugueuse. Nos résultats sont compatibles avec une singularité essentielle exp — C(tR - t) -1/2 suggérée par la relation avec le modèle X Y