2,928 research outputs found
Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model
We investigate the phase diagram of a spin- Ising model on a cubic
lattice, with competing interactions between nearest and next-nearest neighbors
along an axial direction, and fully connected spins on the sites of each
perpendicular layer. The problem is formulated in terms of a set of
noninteracting Ising chains in a position-dependent field. At low temperatures,
as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising
(ANNNI) model, there are many distinct spatially commensurate phases that
spring from a multiphase point of infinitely degenerate ground states. As
temperature increases, we confirm the existence of a branching mechanism
associated with the onset of higher-order commensurate phases. We check that
the ferromagnetic phase undergoes a first-order transition to the modulated
phases. Depending on a parameter of competition, the wave number of the striped
patterns locks in rational values, giving rise to a devil's staircase. We
numerically calculate the Hausdorff dimension associated with these
fractal structures, and show that increases with temperature but seems
to reach a limiting value smaller than .Comment: 17 pages, 6 figure
Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice
We investigate the phase diagram of a discrete version of the Maier-Saupe
model with the inclusion of additional degrees of freedom to mimic a
distribution of rodlike and disklike molecules. Solutions of this problem on a
Bethe lattice come from the analysis of the fixed points of a set of nonlinear
recursion relations. Besides the fixed points associated with isotropic and
uniaxial nematic structures, there is also a fixed point associated with a
biaxial nematic structure. Due to the existence of large overlaps of the
stability regions, we resorted to a scheme to calculate the free energy of
these structures deep in the interior of a large Cayley tree. Both
thermodynamic and dynamic-stability analyses rule out the presence of a biaxial
phase, in qualitative agreement with previous mean-field results
Statistical models of mixtures with a biaxial nematic phase
We consider a simple Maier-Saupe statistical model with the inclusion of
disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like
and disc-like molecules. A quenched distribution of shapes leads to the
existence of a stable biaxial nematic phase, in qualitative agreement with
experimental findings for some ternary lyotropic liquid mixtures. An annealed
distribution, however, which is more adequate to liquid mixtures, precludes the
stability of this biaxial phase. We then use a two-temperature formalism, and
assume a separation of relaxation times, to show that a partial degree of
annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure
A Comprehensive Archival Search for Counterparts to Ultra-Compact High Velocity Clouds: Five Local Volume Dwarf Galaxies
We report five Local Volume dwarf galaxies (two of which are presented here
for the first time) uncovered during a comprehensive archival search for
optical counterparts to ultra-compact high velocity clouds (UCHVCs). The UCHVC
population of HI clouds are thought to be candidate gas-rich, low mass halos at
the edge of the Local Group and beyond, but no comprehensive search for stellar
counterparts to these systems has been presented. Careful visual inspection of
all publicly available optical and ultraviolet imaging at the position of the
UCHVCs revealed six blue, diffuse counterparts with a morphology consistent
with a faint dwarf galaxy beyond the Local Group. Optical spectroscopy of all
six candidate dwarf counterparts show that five have an H-derived
velocity consistent with the coincident HI cloud, confirming their association,
the sixth diffuse counterpart is likely a background object. The size and
luminosity of the UCHVC dwarfs is consistent with other known Local Volume
dwarf irregular galaxies. The gas fraction () of the five
dwarfs are generally consistent with that of dwarf irregular galaxies in the
Local Volume, although ALFALFA-Dw1 (associated with ALFALFA UCHVC
HVC274.68+74.70123) has a very high 40. Despite the
heterogenous nature of our search, we demonstrate that the current dwarf
companions to UCHVCs are at the edge of detectability due to their low surface
brightness, and that deeper searches are likely to find more stellar systems.
If more sensitive searches do not reveal further stellar counterparts to
UCHVCs, then the dearth of such systems around the Local Group may be in
conflict with CDM simulations.Comment: 18 pages, 4 tables, 4 figures, ApJ Accepte
Mutual Information of Population Codes and Distance Measures in Probability Space
We studied the mutual information between a stimulus and a large system
consisting of stochastic, statistically independent elements that respond to a
stimulus. The Mutual Information (MI) of the system saturates exponentially
with system size. A theory of the rate of saturation of the MI is developed. We
show that this rate is controlled by a distance function between the response
probabilities induced by different stimuli. This function, which we term the
{\it Confusion Distance} between two probabilities, is related to the Renyi
-Information.Comment: 11 pages, 3 figures, accepted to PR
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