1,566 research outputs found
Low temperature phase diagram and critical behaviour of the four-state chiral clock model
The low temperature behaviour of the four-state chiral clock () model
is reexamined using a systematic low temperature series expansion of the free
energy. Previously obtained results for the low temperature phases are
corrected and the low temperature phase diagram is derived. In addition, the
phase transition from the modulated region to the high temperature paraphase is
shown to belong to the universality class of the 3d-XY model.Comment: 17 pages in ioplppt style, 3 figure
An Upsilon Point in a Spin Model
We present analytic evidence for the occurrence of an upsilon point, an
infinite checkerboard structure of modulated phases, in the ground state of a
spin model. The structure of the upsilon point is studied by calculating
interface--interface interactions using an expansion in inverse spin
anisotropy.Comment: 18 pages ReVTeX file, including 6 figures encoded with uufile
Lifting of Multiphase Degeneracy by Quantum Fluctuations
We study the effect of quantum fluctuations on the multiphase point of the
Heisenberg model with first- and second-neighbor competing interactions and
strong uniaxial spin anisotropy . By studying the structure of perturbation
theory we show that the multiphase degeneracy which exists for
(i.e., for the ANNNI model) is lifted and that the effect of quantum
fluctuations is to stabilize a sequence of phases of wavelength 4,6,8,...~.
This sequence is probably an infinite one. We also show that quantum
fluctuations can mediate an infinite sequence of layering transitions through
which an interface can unbind from a wall.Comment: 55 pages ReVTeX (encoded with uufiles) + 17 uuencoded figure
Rheology of distorted nematic liquid crystals
We use lattice Boltzmann simulations of the Beris--Edwards formulation of
nematodynamics to probe the response of a nematic liquid crystal with
conflicting anchoring at the boundaries under shear and Poiseuille flow. The
geometry we focus on is that of the hybrid aligned nematic (HAN) cell, common
in devices. In the nematic phase, backflow effects resulting from the elastic
distortion in the director field render the velocity profile strongly
non-Newtonian and asymmetric. As the transition to the isotropic phase is
approached, these effects become progressively weaker. If the fluid is heated
just above the transition point, however, another asymmetry appears, in the
dynamics of shear band formation.Comment: 7 pages, 4 figures. Accepted for publication in Europhys. Let
Vacuum Polarization and Dynamical Chiral Symmetry Breaking: Phase Diagram of QED with Four-Fermion Contact Interaction
We study chiral symmetry breaking for fundamental charged fermions coupled
electromagnetically to photons with the inclusion of four-fermion contact
self-interaction term. We employ multiplicatively renormalizable models for the
photon dressing function and the electron-photon vertex which minimally ensures
mass anomalous dimension = 1. Vacuum polarization screens the interaction
strength. Consequently, the pattern of dynamical mass generation for fermions
is characterized by a critical number of massless fermion flavors above which
chiral symmetry is restored. This effect is in diametrical opposition to the
existence of criticality for the minimum interaction strength necessary to
break chiral symmetry dynamically. The presence of virtual fermions dictates
the nature of phase transition. Miransky scaling laws for the electromagnetic
interaction strength and the four-fermion coupling, observed for quenched QED,
are replaced by a mean-field power law behavior corresponding to a second order
phase transition. These results are derived analytically by employing the
bifurcation analysis, and are later confirmed numerically by solving the
original non-linearized gap equation. A three dimensional critical surface is
drawn to clearly depict the interplay of the relative strengths of interactions
and number of flavors to separate the two phases. We also compute the
beta-function and observe that it has ultraviolet fixed point. The power law
part of the momentum dependence, describing the mass function, reproduces the
quenched limit trivially. We also comment on the continuum limit and the
triviality of QED.Comment: 9 pages, 10 figure
Critical behavior of repulsive linear -mers on triangular lattices
Monte Carlo (MC) simulations and finite-size scaling analysis have been
carried out to study the critical behavior in a submonolayer two-dimensional
gas of repulsive linear -mers on a triangular lattice at coverage
. A low-temperature ordered phase, characterized by a repetition of
alternating files of adsorbed -mers separated by adjacent empty sites,
is separated from the disordered state by a order-disorder phase transition
occurring at a finite critical temperature, . The MC technique was
combined with the recently reported Free Energy Minimization Criterion Approach
(FEMCA), [F. Rom\'a et al., Phys. Rev. B, 68, 205407, (2003)], to predict the
dependence of the critical temperature of the order-disorder transformation.
The dependence on of the transition temperature, , observed in MC
is in qualitative agreement with FEMCA. In addition, an accurate determination
of the critical exponents has been obtained for adsorbate sizes ranging between
and . For , the results reveal that the system does not belong
to the universality class of the two-dimensional Potts model with (,
monomers). Based on symmetry concepts, we suggested that the behavior observed
for and 3 could be generalized to include larger particle sizes ().Comment: 17 pages, 13 figure
Distribution of shortest cycle lengths in random networks
We present analytical results for the distribution of shortest cycle lengths
(DSCL) in random networks. The approach is based on the relation between the
DSCL and the distribution of shortest path lengths (DSPL). We apply this
approach to configuration model networks, for which analytical results for the
DSPL were obtained before. We first calculate the fraction of nodes in the
network which reside on at least one cycle. Conditioning on being on a cycle,
we provide the DSCL over ensembles of configuration model networks with degree
distributions which follow a Poisson distribution (Erdos-R\'enyi network),
degenerate distribution (random regular graph) and a power-law distribution
(scale-free network). The mean and variance of the DSCL are calculated. The
analytical results are found to be in very good agreement with the results of
computer simulations.Comment: 44 pages, 11 figure
Complete wetting in the three-dimensional transverse Ising model
We consider a three-dimensional Ising model in a transverse magnetic field,
and a bulk field . An interface is introduced by an appropriate choice
of boundary conditions. At the point spin configurations
corresponding to different positions of the interface are degenerate. By
studying the phase diagram near this multiphase point using quantum-mechanical
perturbation theory we show that that quantum fluctuations, controlled by ,
split the multiphase degeneracy giving rise to an infinite sequence of layering
transitions.Comment: 16 pages (revtex) including 8 figs; to appear in J. Stat. Phy
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