283 research outputs found
Freezing of Triangulations
Zero temperature dynamics of two dimensional triangulations of a torus with
curvature energy is described. Numerical simulations strongly suggest that the
model get frozen in metastable states, made of topological defects on flat
surfaces, that group into clusters of same topological charge. It is
conjectured that freezing is related to high temperature structure of baby
universes.Comment: 17 pages, 15 figures. 1 section added on connections between present
work and inherent structures ideas; 1 paragraph added in the conclusion; 1
figure added; published versio
Nonperturbative renormalization group approach to Lifshitz critical behaviour
The behaviour of a d-dimensional vectorial N=3 model at a m-axial Lifshitz
critical point is investigated by means of a nonperturbative renormalization
group approach that is free of the huge technical difficulties that plague the
perturbative approaches and limit their computations to the lowest orders. In
particular being systematically improvable, our approach allows us to control
the convergence of successive approximations and thus to get reliable physical
quantities in d=3.Comment: 6 pages, 3 figure
A glassy phase in quenched disordered graphene and crystalline membranes
We investigate the flat phase of -dimensional crystalline membranes
embedded in a -dimensional space and submitted to both metric and curvature
quenched disorders using a nonperturbative renormalization group approach. We
identify a second order phase transition controlled by a finite-temperature,
finite-disorder fixed point unreachable within the leading order of
and expansions. This critical point divides the flow
diagram into two basins of attraction: that associated to the
finite-temperature fixed point controlling the long distance behaviour of
disorder-free membranes and that associated to the zero-temperature,
finite-disorder fixed point. Our work thus strongly suggests the existence of a
whole low-temperature glassy phase for quenched disordered graphene,
graphene-like compounds and, more generally, crystalline membranes.Comment: 6 pages, 1 figur
Robustness of planar random graphs to targeted attacks
In this paper, robustness of planar trivalent random graphs to targeted
attacks of highest connected nodes is investigated using numerical simulations.
It is shown that these graphs are relatively robust. The nonrandom node removal
process of targeted attacks is also investigated as a special case of
non-uniform site percolation. Critical exponents are calculated by measuring
various properties of the distribution of percolation clusters. They are found
to be roughly compatible with critical exponents of uniform percolation on
these graphs.Comment: 9 pages, 11 figures. Added references.Corrected typos. Paragraph
added in section II and in the conclusion. Published versio
Universal behaviors in the wrinkling transition of disordered membranes
The wrinkling transition experimentally identified by Mutz et al. [Phys. Rev.
Lett. 67, 923 (1991)] and then thoroughly studied by Chaieb et al. [Phys. Rev.
Lett. 96, 078101 (2006)] in partially polymerized lipid membranes is
reconsidered. One shows that the features associated with this transition,
notably the various scaling behaviors of the height-height correlation
functions that have been observed, are qualitatively and quantitatively well
described by a recent nonperturbative renormalization group (NPRG) approach to
quenched disordered membranes by Coquand et al. [Phys. Rev E 97, 030102
(2018)]. As these behaviors are associated with fixed points of RG
transformations they are universal and should also be observed in, e.g.,
defective graphene and graphene-like materials.Comment: 6 pages, 2 figures, published versio
Correlation Functions in the Multiple Ising Model Coupled to Gravity
The model of p Ising spins coupled to 2d gravity, in the form of a sum over
planar phi-cubed graphs, is studied and in particular the two-point and
spin-spin correlation functions are considered. We first solve a toy model in
which only a partial summation over spin configurations is performed and, using
a modified geodesic distance, various correlation functions are determined. The
two-point function has a diverging length scale associated with it. The
critical exponents are calculated and it is shown that all the standard scaling
relations apply. Next the full model is studied, in which all spin
configurations are included. Many of the considerations for the toy model apply
for the full model, which also has a diverging geometric correlation length
associated with the transition to a branched polymer phase. Using a transfer
function we show that the two-point and spin-spin correlation functions decay
exponentially with distance. Finally, by assuming various scaling relations, we
make a prediction for the critical exponents at the transition between the
magnetized and branched polymer phases in the full model.Comment: 29 pages, LaTeX, uses epsf macro, 5 figure
On the fractal structure of two-dimensional quantum gravity
We provide evidence that the Hausdorff dimension is 4 and the spectral
dimension is 2 for two-dimensional quantum gravity coupled the matter with a
central charge . For the Hausdorff dimension and the spectral
dimension monotonously decreases to 2 and 1, respectively.Comment: 30 pages, postscript, including 11 figures, csh file.name should
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