30 research outputs found
Isotropic-nematic transition in hard-rod fluids: relation between continuous and restricted-orientation models
We explore models of hard-rod fluids with a finite number of allowed
orientations, and construct their bulk phase diagrams within Onsager's second
virial theory. For a one-component fluid, we show that the discretization of
the orientations leads to the existence of an artificial (almost) perfectly
aligned nematic phase, which coexists with the (physical) nematic phase if the
number of orientations is sufficiently large, or with the isotropic phase if
the number of orientations is small. Its appearance correlates with the
accuracy of sampling the nematic orientation distribution within its typical
opening angle. For a binary mixture this artificial phase also exists, and a
much larger number of orientations is required to shift it to such high
densities that it does not interfere with the physical part of the phase
diagram.Comment: 4 pages, 2 figures, submitted to PR
Buckling Instabilities of a Confined Colloid Crystal Layer
A model predicting the structure of repulsive, spherically symmetric,
monodisperse particles confined between two walls is presented. We study the
buckling transition of a single flat layer as the double layer state develops.
Experimental realizations of this model are suspensions of stabilized colloidal
particles squeezed between glass plates. By expanding the thermodynamic
potential about a flat state of confined colloidal particles, we derive
a free energy as a functional of in-plane and out-of-plane displacements. The
wavevectors of these first buckling instabilities correspond to three different
ordered structures. Landau theory predicts that the symmetry of these phases
allows for second order phase transitions. This possibility exists even in the
presence of gravity or plate asymmetry. These transitions lead to critical
behavior and phases with the symmetry of the three-state and four-state Potts
models, the X-Y model with 6-fold anisotropy, and the Heisenberg model with
cubic interactions. Experimental detection of these structures is discussed.Comment: 24 pages, 8 figures on request. EF508
Nature of the vortex-glass order in strongly type-II superconductors
The stability and the critical properties of the three-dimensional
vortex-glass order in random type-II superconductors with point disorder is
investigated in the unscreened limit based on a lattice {\it XY} model with a
uniform field. By performing equilibrium Monte Carlo simulations for the system
with periodic boundary conditions, the existence of a stable vortex-glass order
is established in the unscreened limit. Estimated critical exponents are
compared with those of the gauge-glass model.Comment: Error in the reported value of the exponent eta is correcte
Transport on percolation clusters with power-law distributed bond strengths: when do blobs matter?
The simplest transport problem, namely maxflow, is investigated on critical
percolation clusters in two and three dimensions, using a combination of
extremal statistics arguments and exact numerical computations, for power-law
distributed bond strengths of the type .
Assuming that only cutting bonds determine the flow, the maxflow critical
exponent \ve is found to be \ve(\alpha)=(d-1) \nu + 1/(1-\alpha). This
prediction is confirmed with excellent accuracy using large-scale numerical
simulation in two and three dimensions. However, in the region of anomalous
bond capacity distributions () we demonstrate that, due to
cluster-structure fluctuations, it is not the cutting bonds but the blobs that
set the transport properties of the backbone. This ``blob-dominance'' avoids a
cross-over to a regime where structural details, the distribution of the number
of red or cutting bonds, would set the scaling. The restored scaling exponents
however still follow the simplistic red bond estimate. This is argued to be due
to the existence of a hierarchy of so-called minimum cut-configurations, for
which cutting bonds form the lowest level, and whose transport properties scale
all in the same way. We point out the relevance of our findings to other scalar
transport problems (i.e. conductivity).Comment: 9 pages + Postscript figures. Revtex4+psfig. Submitted to PR
Segregated tunneling-percolation model for transport nonuniversality
We propose a theory of the origin of transport nonuniversality in disordered
insulating-conducting compounds based on the interplay between microstructure
and tunneling processes between metallic grains dispersed in the insulating
host. We show that if the metallic phase is arranged in quasi-one dimensional
chains of conducting grains, then the distribution function of the chain
conductivities g has a power-law divergence for g -> 0 leading to nonuniversal
values of the transport critical exponent t. We evaluate the critical exponent
t by Monte Carlo calculations on a cubic lattice and show that our model can
describe universal as well nonuniversal behavior of transport depending on the
value of few microstructural parameters. Such segregated tunneling-percolation
model can describe the microstructure of a quite vast class of materials known
as thick-film resistors which display universal or nonuniversal values of t
depending on the composition.Comment: 8 pages, 5 figures (Phys. Rev. B - 1 August 2003)(fig1 replaced
Tunneling and the Spectrum of the Potts Model
The three-dimensional, three-state Potts model is studied as a paradigm for
high temperature quantum chromodynamics. In a high statistics numerical
simulation using a Swendson-Wang algorithm, we study cubic lattices of
dimension as large as and measure correlation functions on long lattices
of dimension and . These correlations are
controlled by the spectrum of the transfer matrix. This spectrum is studied in
the vicinity of the phase transition. The analysis classifies the spectral
levels according to an underlying symmetry. Near the phase transition the
spectrum agrees nicely with a simple four-component hamiltonian model. In the
context of this model, we find that low temperature ordered-ordered interfaces
nearly always involve a disordered phase intermediate. We present a new
spectral method for determining the surface tension between phases.Comment: 26 pages plus 13 Postscript figures (Axis versions also provided),
UU-HEP-92/
Frustrated two-dimensional Josephson junction array near incommensurability
To study the properties of frustrated two-dimensional Josephson junction
arrays near incommensurability, we examine the current-voltage characteristics
of a square proximity-coupled Josephson junction array at a sequence of
frustrations f=3/8, 8/21, 0.382 , 2/5, and 5/12.
Detailed scaling analyses of the current-voltage characteristics reveal
approximately universal scaling behaviors for f=3/8, 8/21, 0.382, and 2/5. The
approximately universal scaling behaviors and high superconducting transition
temperatures indicate that both the nature of the superconducting transition
and the vortex configuration near the transition at the high-order rational
frustrations f=3/8, 8/21, and 0.382 are similar to those at the nearby simple
frustration f=2/5. This finding suggests that the behaviors of Josephson
junction arrays in the wide range of frustrations might be understood from
those of a few simple rational frustrations.Comment: RevTex4, 4 pages, 4 eps figures, to appear in Phys. Rev.
Two-species percolation and Scaling theory of the metal-insulator transition in two dimensions
Recently, a simple non-interacting-electron model, combining local quantum
tunneling via quantum point contacts and global classical percolation, has been
introduced in order to describe the observed ``metal-insulator transition'' in
two dimensions [1]. Here, based upon that model, a two-species-percolation
scaling theory is introduced and compared to the experimental data. The two
species in this model are, on one hand, the ``metallic'' point contacts, whose
critical energy lies below the Fermi energy, and on the other hand, the
insulating quantum point contacts. It is shown that many features of the
experiments, such as the exponential dependence of the resistance on
temperature on the metallic side, the linear dependence of the exponent on
density, the scale of the critical resistance, the quenching of the
metallic phase by a parallel magnetic field and the non-monotonic dependence of
the critical density on a perpendicular magnetic field, can be naturally
explained by the model.
Moreover, details such as the nonmonotonic dependence of the resistance on
temperature or the inflection point of the resistance vs. parallel magnetic are
also a natural consequence of the theory. The calculated parallel field
dependence of the critical density agrees excellently with experiments, and is
used to deduce an experimental value of the confining energy in the vertical
direction. It is also shown that the resistance on the ``metallic'' side can
decrease with decreasing temperature by an arbitrary factor in the degenerate
regime ().Comment: 8 pages, 8 figure