62 research outputs found
Effects of Self-Avoidance on the Tubular Phase of Anisotropic Membranes
We study the tubular phase of self-avoiding anisotropic membranes. We discuss
the renormalizability of the model Hamiltonian describing this phase and derive
from a renormalization group equation some general scaling relations for the
exponents of the model. We show how particular choices of renormalization
factors reproduce the Gaussian result, the Flory theory and the Gaussian
Variational treatment of the problem. We then study the perturbative
renormalization to one loop in the self-avoiding parameter using dimensional
regularization and an epsilon-expansion about the upper critical dimension, and
determine the critical exponents to first order in epsilon.Comment: 19 pages, TeX, uses Harvmac. Revised Title and updated references: to
appear in Phys. Rev.
Fluctuating Nematic Elastomer Membranes: a New Universality Class
We study the flat phase of nematic elastomer membranes with rotational
symmetry spontaneously broken by in-plane nematic order. Such state is
characterized by a vanishing elastic modulus for simple shear and soft
transverse phonons. At harmonic level, in-plane orientational (nematic) order
is stable to thermal fluctuations, that lead to short-range in-plane
translational (phonon) correlations. To treat thermal fluctuations and relevant
elastic nonlinearities, we introduce two generalizations of two-dimensional
membranes in a three dimensional space to arbitrary D-dimensional membranes
embedded in a d-dimensional space, and analyze their anomalous elasticities in
an expansion about D=4. We find a new stable fixed point, that controls
long-scale properties of nematic elastomer membranes. It is characterized by
singular in-plane elastic moduli that vanish as a power-law eta_lambda=4-D of a
relevant inverse length scale (e.g., wavevector) and a finite bending rigidity.
Our predictions are asymptotically exact near 4 dimensions.Comment: 18 pages, 4 eps figures. submitted to PR
Folding of the Triangular Lattice with Quenched Random Bending Rigidity
We study the problem of folding of the regular triangular lattice in the
presence of a quenched random bending rigidity + or - K and a magnetic field h
(conjugate to the local normal vectors to the triangles). The randomness in the
bending energy can be understood as arising from a prior marking of the lattice
with quenched creases on which folds are favored. We consider three types of
quenched randomness: (1) a ``physical'' randomness where the creases arise from
some prior random folding; (2) a Mattis-like randomness where creases are
domain walls of some quenched spin system; (3) an Edwards-Anderson-like
randomness where the bending energy is + or - K at random independently on each
bond. The corresponding (K,h) phase diagrams are determined in the hexagon
approximation of the cluster variation method. Depending on the type of
randomness, the system shows essentially different behaviors.Comment: uses harvmac (l), epsf, 17 figs included, uuencoded, tar compresse
Folding transition of the triangular lattice in a discrete three--dimensional space
A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E.
Guitter (cond-mat/9502063) describing the folding of the triangular lattice
onto the face centered cubic lattice has been studied in the hexagon
approximation of the cluster variation method. The model describes the
behaviour of a polymerized membrane in a discrete three--dimensional space. We
have introduced a curvature energy and a symmetry breaking field and studied
the phase diagram of the resulting model. By varying the curvature energy
parameter, a first-order transition has been found between a flat and a folded
phase for any value of the symmetry breaking field.Comment: 11 pages, latex file, 2 postscript figure
Universal Negative Poisson Ratio of Self Avoiding Fixed Connectivity Membranes
We determine the Poisson ratio of self-avoiding fixed-connectivity membranes,
modeled as impenetrable plaquettes, to be sigma=-0.37(6), in statistical
agreement with the Poisson ratio of phantom fixed-connectivity membranes
sigma=-0.32(4). Together with the equality of critical exponents, this result
implies a unique universality class for fixed-connectivity membranes. Our
findings thus establish that physical fixed-connectivity membranes provide a
wide class of auxetic (negative Poisson ratio) materials with significant
potential applications in materials science.Comment: 4 pages, 3 figures, LaTeX (revtex) Published version - title changed,
one figure improved and one reference change
Topological Defects on Fluctuating Surfaces: General Properties and the Kosterlitz-Thouless Transition
We investigate the Kosterlitz-Thouless transition for hexatic order on a free
fluctuating membrane and derive both a Coulomb gas and a sine-Gordon
Hamiltonian to describe it. The Coulomb-gas Hamiltonian includes charge
densities arising from disclinations and from Gaussian curvature. There is an
interaction coupling the difference between these two densities, whose strength
is determined by the hexatic rigidity, and an interaction coupling Gaussian
curvature densities arising from the Liouville Hamiltonian resulting from the
imposition of a covariant cutoff. In the sine-Gordon Hamiltonian, there is a
linear coupling between a scalar field and the Gaussian curvature. We discuss
gauge-invariant correlation function for hexatic order and the dielectric
constant of the Coulomb gas. We also derive renormalization group recursion
relations that predict a transition with decreasing bending rigidity .Comment: REVTEX, 45 pages with 11 postscript figures compressed using uufiles.
Accepted for publication in Phys. Rev.
Fluctuations of elastic interfaces in fluids: Theory and simulation
We study the dynamics of elastic interfaces-membranes-immersed in thermally
excited fluids. The work contains three components: the development of a
numerical method, a purely theoretical approach, and numerical simulation. In
developing a numerical method, we first discuss the dynamical coupling between
the interface and the surrounding fluids. An argument is then presented that
generalizes the single-relaxation time lattice-Boltzmann method for the
simulation of hydrodynamic interfaces to include the elastic properties of the
boundary. The implementation of the new method is outlined and it is tested by
simulating the static behavior of spherical bubbles and the dynamics of bending
waves. By means of the fluctuation-dissipation theorem we recover analytically
the equilibrium frequency power spectrum of thermally fluctuating membranes and
the correlation function of the excitations. Also, the non-equilibrium scaling
properties of the membrane roughening are deduced, leading us to formulate a
scaling law describing the interface growth, W^2(L,T)=L^3 g[t/L^(5/2)], where
W, L and T are the width of the interface, the linear size of the system and
the temperature respectively, and g is a scaling function. Finally, the
phenomenology of thermally fluctuating membranes is simulated and the frequency
power spectrum is recovered, confirming the decay of the correlation function
of the fluctuations. As a further numerical study of fluctuating elastic
interfaces, the non-equilibrium regime is reproduced by initializing the system
as an interface immersed in thermally pre-excited fluids.Comment: 15 pages, 11 figure
Folding transitions of the triangular lattice with defects
A recently introduced model describing the folding of the triangular lattice
is generalized allowing for defects in the lattice and written as an Ising
model with nearest-neighbor and plaquette interactions on the honeycomb
lattice. Its phase diagram is determined in the hexagon approximation of the
cluster variation method and the crossover from the pure Ising to the pure
folding model is investigated, obtaining a quite rich structure with several
multicritical points. Our results are in very good agreement with the available
exact ones and extend a previous transfer matrix study.Comment: 16 pages, latex, 5 postscript figure
Levy flights in quenched random force fields
Levy flights, characterized by the microscopic step index f, are for f<2 (the
case of rare events) considered in short range and long range quenched random
force fields with arbitrary vector character to first loop order in an
expansion about the critical dimension 2f-2 in the short range case and the
critical fall-off exponent 2f-2 in the long range case. By means of a dynamic
renormalization group analysis based on the momentum shell integration method,
we determine flows, fixed point, and the associated scaling properties for the
probability distribution and the frequency and wave number dependent diffusion
coefficient. Unlike the case of ordinary Brownian motion in a quenched force
field characterized by a single critical dimension or fall-off exponent d=2,
two critical dimensions appear in the Levy case. A critical dimension (or
fall-off exponent) d=f below which the diffusion coefficient exhibits anomalous
scaling behavior, i.e, algebraic spatial behavior and long time tails, and a
critical dimension (or fall-off exponent) d=2f-2 below which the force
correlations characterized by a non trivial fixed point become relevant. As a
general result we find in all cases that the dynamic exponent z, characterizing
the mean square displacement, locks onto the Levy index f, independent of
dimension and independent of the presence of weak quenched disorder.Comment: 27 pages, Revtex file, 17 figures in ps format attached, submitted to
Phys. Rev.
Large times off-equilibrium dynamics of a particle in a random potential
We study the off-equilibrium dynamics of a particle in a general
-dimensional random potential when . We demonstrate the
existence of two asymptotic time regimes: {\it i.} stationary dynamics, {\it
ii.} slow aging dynamics with violation of equilibrium theorems. We derive the
equations obeyed by the slowly varying part of the two-times correlation and
response functions and obtain an analytical solution of these equations. For
short-range correlated potentials we find that: {\it i.} the scaling function
is non analytic at similar times and this behaviour crosses over to
ultrametricity when the correlations become long range, {\it ii.} aging
dynamics persists in the limit of zero confining mass with universal features
for widely separated times. We compare with the numerical solution to the
dynamical equations and generalize the dynamical equations to finite by
extending the variational method to the dynamics.Comment: 70 pages, 7 figures included, uuencoded Z-compressed .tar fil
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