33 research outputs found
Surface extrapolation length and director structures in confined nematics
We report the results of Monte Carlo simulations of the Lebwohl--Lasher model
of nematic liquid crystals confined to cylindrical cavities with homeotropic
anchoring. We show that the ratio of the bulk to surface couplings is not in
general equal to the corresponding parameter K/W used in elastic theory (where
K is the Frank elastic constant in the one constant approximation and W is the
surface anchoring strength). By measuring the temperature dependence of K/W
(which is equivalent to the surface extrapolation length) we are able to
reconcile the results of our simulations as well as others with the predictions
of elastic theory. We find that the rate at which we cool the system from the
isotropic to nematic phase plays a crucial role in the development of the final
director structure, because of a large free energy barrier separating different
director structures as well as the temperature dependence of . With a
suitably fast cooling rate we are able to keep the system out of a metastable
planar state and form an escaped radial structure for large enough systems.Comment: 6 pages, 5 figure
Monte Carlo simulations of , a classical Heisenberg antiferromagnet in two-dimensions with dipolar interaction
We study the phase diagram of a quasi-two dimensional magnetic system with Monte Carlo simulations of a classical Heisenberg spin
Hamiltonian which includes the dipolar interactions between
spins. Our simulations reveal an Ising-like antiferromagnetic phase at low
magnetic fields and an XY phase at high magnetic fields. The boundary between
Ising and XY phases is analyzed with a recently proposed finite size scaling
technique and found to be consistent with a bicritical point at T=0. We discuss
the computational techniques used to handle the weak dipolar interaction and
the difference between our phase diagram and the experimental results.Comment: 13 pages 18 figure
Cluster Monte Carlo Simulations of the Nematic--Isotropic Transition
We report the results of simulations of the Lebwohl-Lasher model of the
nematic-isotropic transition using a new cluster Monte Carlo algorithm. The
algorithm is a modification of the Wolff algorithm for spin systems, and
greatly reduces critical slowing down. We calculate the free energy in the
neighborhood of the transition for systems up to linear size 70. We find a
double well structure with a barrier that grows with increasing system size,
obeying finite size scaling for systems of size greater than 35. We thus obtain
an estimate of the value of the transition temperature in the thermodynamic
limit.Comment: 4 figure
O(4)-Invariant Formulation of the Nodal Liquid
We consider the O(4) symmetric point in the phase diagram of an electron
system in which there is a transition between d_{x^2 - y^2} density-wave order
and d_{x^2 - y^2} superconductivity. If the pseudospin
symmetry is disordered by quantum fluctuations, the Nodal Liquid can result. In
this context, we (1) construct a pseudospin -model; (2) discuss its
topological excitations; (3) point out the possibility of a {\it
pseudospin-Peierls} state and (4) propose a phase diagram for the underdoped
cuprate superconductors
Randomly dilute Ising model: A nonperturbative approach
The N-vector cubic model relevant, among others, to the physics of the
randomly dilute Ising model is analyzed in arbitrary dimension by means of an
exact renormalization-group equation. This study provides a unified picture of
its critical physics between two and four dimensions. We give the critical
exponents for the three-dimensional randomly dilute Ising model which are in
good agreement with experimental and numerical data. The relevance of the cubic
anisotropy in the O(N) model is also treated.Comment: 4 pages, published versio
Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
The critical thermodynamics of the two-dimensional N-vector cubic and MN
models is studied within the field-theoretical renormalization-group (RG)
approach. The beta functions and critical exponents are calculated in the
five-loop approximation and the RG series obtained are resummed using the
Borel-Leroy transformation combined with the generalized Pad\'e approximant and
conformal mapping techniques. For the cubic model, the RG flows for various N
are investigated. For N=2 it is found that the continuous line of fixed points
running from the XY fixed point to the Ising one is well reproduced by the
resummed RG series and an account for the five-loop terms makes the lines of
zeros of both beta functions closer to each another. For the cubic model with
N\geq 3, the five-loop contributions are shown to shift the cubic fixed point,
given by the four-loop approximation, towards the Ising fixed point. This
confirms the idea that the existence of the cubic fixed point in two dimensions
under N>2 is an artifact of the perturbative analysis. For the quenched dilute
O(M) models ( models with N=0) the results are compatible with a stable
pure fixed point for M\geq1. For the MN model with M,N\geq2 all the
non-perturbative results are reproduced. In addition a new stable fixed point
is found for moderate values of M and N.Comment: 26 pages, 3 figure
Phase-transitions induced by easy-plane anisotropy in the classical Heisenberg antiferromagnet on a triangular lattice: a Monte Carlo simulation
We present the results of Monte Carlo simulations for the antiferromagnetic
classical XXZ model with easy-plane exchange anisotropy on the triangular
lattice, which causes frustration of the spin alignment. The behaviour of this
system is similar to that of the antiferromagnetic XY model on the same
lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition,
associated to vortex-antivortex unbinding, and of an Ising-like one due to the
chirality, the latter occurring at a slightly higher temperature. Data for
internal energy, specific heat, magnetic susceptibility, correlation length,
and some properties associated with the chirality are reported in a broad
temperature range, for lattice sizes ranging from 24x24 to 120x120; four values
of the easy-plane anisotropy are considered. Moving from the strongest towards
the weakest anisotropy (1%) the thermodynamic quantities tend to the isotropic
model behaviour, and the two transition temperatures decrease by about 25% and
22%, respectively.Comment: 11 pages, 13 figures (embedded by psfig), 3 table
Long Wavelength Anomalous Diffusion Mode in the 2D XY Dipole Magnet
In 2D XY ferromagnet the dipole force induces a strong interaction between
spin-waves in the long-wavelength limit. The major effect of this interaction
is the transformation of a propagating spin-wave into a diffusion mode. We
study the anomalous dynamics of such diffusion modes. We find that the
Janssen-De Dominics functional, which governs this dynamics, approaches the
non-Gaussian fixed-point. A spin-wave propagates by an anomalous anisotropic
diffusion with the dispersion relation: and
, where and
. The low-frequency response to the external magnetic field
is found.Comment: 34 pages, RevTeX, 2 .ps figures, the third figure is available upon
reques
Phase-ordering dynamics of the Gay-Berne nematic liquid crystal
Phase-ordering dynamics in nematic liquid crystals has been the subject of
much active investigation in recent years in theory, experiments and
simulations. With a rapid quench from the isotropic to nematic phase a large
number of topological defects are formed and dominate the subsequent
equilibration process. We present here the results of a molecular dynamics
simulation of the Gay-Berne model of liquid crystals after such a quench in a
system with 65536 molecules. Twist disclination lines as well as type-1 lines
and monopoles were observed. Evidence of dynamical scaling was found in the
behavior of the spatial correlation function and the density of disclination
lines. However, the behavior of the structure factor provides a more sensitive
measure of scaling, and we observed a crossover from a defect dominated regime
at small values of the wavevector to a thermal fluctuation dominated regime at
large wavevector.Comment: 18 pages, 16 figures, animations available at
http://www.physics.brown.edu/Users/faculty/pelcovits/lc/coarsening.htm
Critical equation of state of randomly dilute Ising systems
We determine the critical equation of state of three-dimensional randomly
dilute Ising systems, i.e. of the random-exchange Ising universality class. We
first consider the small-magnetization expansion of the Helmholtz free energy
in the high-temperature phase. Then, we apply a systematic approximation scheme
of the equation of state in the whole critical regime, that is based on
polynomial parametric representations matching the small-magnetization of the
Helmholtz free energy and satisfying a global stationarity condition. These
results allow us to estimate several universal amplitude ratios, such as the
ratio A^+/A^- of the specific-heat amplitudes. Our best estimate A^+/A^-=1.6(3)
is in good agreement with experimental results on dilute uniaxial
antiferromagnets.Comment: 21 pages, 1 figure, refs adde