111 research outputs found
Connecting the vulcanization transition to percolation
The vulcanization transition is addressed via a minimal
replica-field-theoretic model. The appropriate long-wave-length behavior of the
two- and three-point vertex functions is considered diagrammatically, to all
orders in perturbation theory, and identified with the corresponding quantities
in the Houghton-Reeve-Wallace field-theoretic approach to the percolation
critical phenomenon. Hence, it is shown that percolation theory correctly
captures the critical phenomenology of the vulcanization transition associated
with the liquid and critical states.Comment: 9 pages, 5 figure
Scaling behaviour of lattice animals at the upper critical dimension
We perform numerical simulations of the lattice-animal problem at the upper
critical dimension d=8 on hypercubic lattices in order to investigate
logarithmic corrections to scaling there. Our stochastic sampling method is
based on the pruned-enriched Rosenbluth method (PERM), appropriate to linear
polymers, and yields high statistics with animals comprised of up to 8000
sites. We estimate both the partition sums (number of different animals) and
the radii of gyration. We re-verify the Parisi-Sourlas prediction for the
leading exponents and compare the logarithmic-correction exponents to two
partially differing sets of predictions from the literature. Finally, we
propose, and test, a new Parisi-Sourlas-type scaling relation appropriate for
the logarithmic-correction exponents.Comment: 10 pages, 5 figure
Nematic Films and Radially Anisotropic Delaunay Surfaces
We develop a theory of axisymmetric surfaces minimizing a combination of
surface tension and nematic elastic energies which may be suitable for
describing simple film and bubble shapes. As a function of the elastic constant
and the applied tension on the bubbles, we find the analogues of the unduloid,
sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure
Theory of Chiral Modulations and Fluctuations in Smectic-A Liquid Crystals Under an Electric Field
Chiral liquid crystals often exhibit periodic modulations in the molecular
director; in particular, thin films of the smectic-C* phase show a chiral
striped texture. Here, we investigate whether similar chiral modulations can
occur in the induced molecular tilt of the smectic-A phase under an applied
electric field. Using both continuum elastic theory and lattice simulations, we
find that the state of uniform induced tilt can become unstable when the system
approaches the smectic-A--smectic-C* transition, or when a high electric field
is applied. Beyond that instability point, the system develops chiral stripes
in the tilt, which induce corresponding ripples in the smectic layers. The
modulation persists up to an upper critical electric field and then disappears.
Furthermore, even in the uniform state, the system shows chiral fluctuations,
including both incipient chiral stripes and localized chiral vortices. We
compare these predictions with observed chiral modulations and fluctuations in
smectic-A liquid crystals.Comment: 11 pages, including 9 postscript figures, uses REVTeX 3.0 and
epsf.st
The Structure of TGB Phases
We study the transition from the cholesteric phase to two TGB phases near
the upper critical twist : the Renn-Lubensky TGB phase, with layer
normal rotating in a plane perpendicular to the pitch axis, and the Bordeaux
TGB phase, with the layer normal rotating on a cone parallel to the pitch
axis. We calculate properties, including order-parameter profiles, of both
phases.Comment: 4 pages, 4 figures, Submitted to Physical Review E, Rapid
Communications, September 5, 2003; Revised manuscript (to the paper submitted
on March 18, 2003, cond-mat/0303365)that includes an important missing
reference and presents an improved analysis of a generalized mode
Mechanical Weyl Modes in Topological Maxwell Lattices
Theoretical Physic
Universality Class of Thermally Diluted Ising Systems at Criticality
The universality class of thermally diluted Ising systems, in which the
realization of the disposition of magnetic atoms and vacancies is taken from
the local distribution of spins in the pure original Ising model at
criticality, is investigated by finite size scaling techniques using the Monte
Carlo method. We find that the critical temperature, the critical exponents and
therefore the universality class of these thermally diluted Ising systems
depart markedly from the ones of short range correlated disordered systems. Our
results agree fairly well with theoretical predictions previously made by
Weinrib and Halperin for systems with long range correlated disorder.Comment: 7 pages, 6 figures, RevTe
Distribution of the area enclosed by a 2D random walk in a disordered medium
The asymptotic probability distribution for a Brownian particle wandering in
a 2D plane with random traps to enclose the algebraic area A by time t is
calculated using the instanton technique.Comment: 4 pages, ReVTeX. Phys. Rev. E (March 1999), to be publishe
Effective index of refraction, optical rotation, and circular dichroism in isotropic chiral liquid crystals
This paper concerns optical properties of the isotropic phase above the
isotropic-cholesteric transition and of the blue phase BP III. We introduce an
effective index, which describes spatial dispersion effects such as optical
rotation, circular dichroism, and the modification of the average index due to
the fluctuations. We derive the wavelength dependance of these spatial
dispersion effects quite generally without relying on an expansion in powers of
the chirality and without assuming that the pitch of the cholesteric is
much shorter than the wavelength of the light , an approximation which
has been made in previous studies of this problem. The theoretical predictions
are supported by comparing them with experimental spectra of the optical
activity in the BP III phase.Comment: 15 pages and 7 figures. Submitted to PR
Correlated disordered interactions on Potts models
Using a weak-disorder scheme and real-space renormalization-group techniques,
we obtain analytical results for the critical behavior of various q-state Potts
models with correlated disordered exchange interactions along d1 of d spatial
dimensions on hierarchical (Migdal-Kadanoff) lattices. Our results indicate
qualitative differences between the cases d-d1=1 (for which we find nonphysical
random fixed points, suggesting the existence of nonperturbative fixed
distributions) and d-d1>1 (for which we do find acceptable perturbartive random
fixed points), in agreement with previous numerical calculations by Andelman
and Aharony. We also rederive a criterion for relevance of correlated disorder,
which generalizes the usual Harris criterion.Comment: 8 pages, 4 figures, to be published in Physical Review
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