705 research outputs found
The Poisson ratio of crystalline surfaces
A remarkable theoretical prediction for a crystalline (polymerized) surface
is that its Poisson ratio (\sigma) is negative. Using a large scale Monte Carlo
simulation of a simple model of such surfaces we show that this is indeed true.
The precise numerical value we find is (\sigma \simeq -0.32) on a (128^2)
lattice at bending rigidity (kappa = 1.1). This is in excellent agreement with
the prediction (\sigma = -1/3) following from the self-consistent screening
approximation of Le Doussal and Radzihovsky.Comment: 7 pages, 2 EPS figures, LaTeX2e. Revised version accepted for
publication on Europhys. Let
Monte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter
We extend a recently proposed real-space renormalization group scheme for
dynamical triangulations to situations where the lattice is coupled to
continuous scalar fields. Using Monte Carlo simulations in combination with a
linear, stochastic blocking scheme for the scalar fields we are able to
determine the leading eigenvalues of the stability matrix with good accuracy
both for c = 1 and c = 10 theories.Comment: 17 pages, 7 figure
Unsupervised empirical Bayesian multiple testing with external covariates
In an empirical Bayesian setting, we provide a new multiple testing method,
useful when an additional covariate is available, that influences the
probability of each null hypothesis being true. We measure the posterior
significance of each test conditionally on the covariate and the data, leading
to greater power. Using covariate-based prior information in an unsupervised
fashion, we produce a list of significant hypotheses which differs in length
and order from the list obtained by methods not taking covariate-information
into account. Covariate-modulated posterior probabilities of each null
hypothesis are estimated using a fast approximate algorithm. The new method is
applied to expression quantitative trait loci (eQTL) data.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS158 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Anisotropic Membranes
We describe the statistical behavior of anisotropic crystalline membranes. In
particular we give the phase diagram and critical exponents for phantom
membranes and discuss the generalization to self-avoiding membranes.Comment: LATTICE98(surfaces) 5 pages, 4 Postscript figure
Universality Classes of Self-Avoiding Fixed-Connectivity Membranes
We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. We simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we find the membrane to be flat for all temperatures: the size exponent in three dimensions is nu=0.95(5) (Hausdorff dimension d_H=2.1(1)). The single flat phase appears, furthermore, to be equivalent to the large bending rigidity phase of non-self-avoiding fixed-connectivity membranes - the roughness exponent in three dimensions is xi=0.63(4). This suggests that there is a unique universality class for flat fixed-connectivity membranes without attractive interactions. Finally we address some theoretical and experimental implications of our work
Minimal Dynamical Triangulations of Random Surfaces
We introduce and investigate numerically a minimal class of dynamical
triangulations of two-dimensional gravity on the sphere in which only vertices
of order five, six or seven are permitted. We show firstly that this
restriction of the local coordination number, or equivalently intrinsic scalar
curvature, leaves intact the fractal structure characteristic of generic
dynamically triangulated random surfaces. Furthermore the Ising model coupled
to minimal two-dimensional gravity still possesses a continuous phase
transition. The critical exponents of this transition correspond to the usual
KPZ exponents associated with coupling a central charge c=1/2 model to
two-dimensional gravity.Comment: Latex, 9 pages, 3 figures, Published versio
New critical phenomena in 2d quantum gravity
We study and state Potts models on dynamical triangulated
lattices and demonstrate that these models exhibit continuous phase
transitions, contrary to the first order transition present on regular
lattices. For the transition seems to be of 2nd order, while it seems to
be of 3rd order for . For the phase transition also induces a
transition between typical fractal structures of the piecewise linear surfaces
corresponding to the triangulations. The typical surface changes from having a
tree-like structure to a fractal structure characterizing pure gravity when the
temperature drops below the critical temperature. An investigation of the
alignment of spin clusters shows that they are strongly correlated to the
underlying fractal structure of the triangulated surfaces.Comment: 22 pages, uuencoded compressed ps-file. Use csh file.uu to get
ps-fil
Numerical Observation of a Tubular Phase in Anisotropic Membranes
We provide the first numerical evidence for the existence of a tubular phase,
predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes
without self-avoidance. Incorporating anisotropy into the bending rigidity of a
simple model of a tethered membrane with free boundary conditions, we show that
the model indeed has two phase transitions corresponding to the flat-to-tubular
and tubular-to-crumpled transitions. For the tubular phase we measure the Flory
exponent and the roughness exponent . We find
and , which are in reasonable agreement with the theoretical
predictions of RT --- and .Comment: 8 pages, LaTeX, REVTEX, final published versio
A Universal Fractal Structure of 2D Quantum Gravity for c > 1
We investigate the fractal structure of quantum gravity coupled to
matter by measuring the distributions of so-called baby universes. We
demonstrate that the method works well as long as . For it is
not clear what distribution to expect. However, we observe strikingly similar
distributions for various kinds of matter fields with the same . This
indicate that there might be some range of where the central charge of
the matter fields alone determines the fractal structure of gravity coupled to
matter. The hypothesis that the string susceptibility \g = 1/3 is found to be
compatible with the data for .Comment: 12 pages. compressed postscript file. Uncompressed size 3 Mb. Latex
file without figures available by request. NBI-HE-93-6
Simulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations
We extend a model of four-dimensional simplicial quantum gravity to include
degenerate triangulations in addition to combinatorial triangulations
traditionally used. Relaxing the constraint that every 4-simplex is uniquely
defined by a set of five distinct vertexes, we allow triangulations containing
multiply connected simplexes and distinct simplexes defined by the same set of
vertexes. We demonstrate numerically that including degenerated triangulations
substantially reduces the finite-size effects in the model. In particular, we
provide a strong numerical evidence for an exponential bound on the entropic
growth of the ensemble of degenerate triangulations, and show that a
discontinuous crumpling transition is already observed on triangulations of
volume N_4 ~= 4000.Comment: Latex, 8 pages, 4 eps-figure
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