276 research outputs found
Interfering directed paths and the sign phase transition
We revisit the question of the "sign phase transition" for interfering
directed paths with real amplitudes in a random medium. The sign of the total
amplitude of the paths to a given point may be viewed as an Ising order
parameter, so we suggest that a coarse-grained theory for system is a dynamic
Ising model coupled to a Kardar-Parisi-Zhang (KPZ) model. It appears that when
the KPZ model is in its strong-coupling ("pinned") phase, the Ising model does
not have a stable ferromagnetic phase, so there is no sign phase transition. We
investigate this numerically for the case of {\ss}1+1 dimensions, demonstrating
the instability of the Ising ordered phase there.Comment: 4 pages, 4 figure
Anomaly-Free Sets of Fermions
We present new techniques for finding anomaly-free sets of fermions. Although
the anomaly cancellation conditions typically include cubic equations with
integer variables that cannot be solved in general, we prove by construction
that any chiral set of fermions can be embedded in a larger set of fermions
which is chiral and anomaly-free. Applying these techniques to extensions of
the Standard Model, we find anomaly-free models that have arbitrary quark and
lepton charges under an additional U(1) gauge group.Comment: 21 (+1) page
California\u27s Recall Is Not Overpowered
The recall is one of three direct democracy tools in California. Following the failed 2021 recall attempt against California Governor Gavin Newsom, the state recall process has been criticized for evolving beyond its intended purpose to the point of being overpowered and prone to abuse. After reviewing the recall’s original intent, we conduct a quantitative analysis of state and local recall attempts in California and compare this to other recall states. We conclude that the critique is unjustified. In California and elsewhere, state official recalls are frequently attempted but rarely qualify for the ballot, demonstrating that the existing recall system is an effective filter. We validate the charge that the recall is primarily a tool of out-party interests, but conclude that this is an intended design feature rather than an unanticipated defect. We conclude instead that California’s local recall is the better target for reform efforts, given its comparatively easier qualifying requirements, greater use, and higher success rates. Rather than deviating from its intended purpose, in its 110 years the California state official recall proved to be exactly what its Progressive designers intended: a voter weapon to menace and remove public officials, but one that is difficult to deploy. We frame the recall as less about politics and more about policy: recalls function as public opinion or policy polls and overall tend to validate existing policy. Finally, we conclude that most proposed reforms are solutions seeking a problem, and that California’s recall system merits just a few small procedural changes. The upshot is that the view of California’s recall as a force gone amok is incorrect
n-atic Order and Continuous Shape Changes of Deformable Surfaces of Genus Zero
We consider in mean-field theory the continuous development below a
second-order phase transition of -atic tangent plane order on a deformable
surface of genus zero with order parameter . Tangent plane order expels Gaussian curvature. In addition, the total
vorticity of orientational order on a surface of genus zero is two. Thus, the
ordered phase of an -atic on such a surface will have vortices of
strength , zeros in its order parameter, and a nonspherical
equilibrium shape. Our calculations are based on a phenomenological model with
a gauge-like coupling between and curvature, and our analysis follows
closely the Abrikosov treatment of a type II superconductor just below
.Comment: REVTEX, 12 page
Defect generation and deconfinement on corrugated topographies
We investigate topography-driven generation of defects in liquid crystals
films coating frozen surfaces of spatially varying Gaussian curvature whose
topology does not automatically require defects in the ground state. We study
in particular disclination-unbinding transitions with increasing aspect ratio
for a surface shaped as a Gaussian bump with an hexatic phase draped over it.
The instability of a smooth ground state texture to the generation of a single
defect is also discussed. Free boundary conditions for a single bump are
considered as well as periodic arrays of bumps. Finally, we argue that defects
on a bump encircled by an aligning wall undergo sharp deconfinement transitions
as the aspect ratio of the surface is lowered.Comment: 24 page
Membrane geometry with auxiliary variables and quadratic constraints
Consider a surface described by a Hamiltonian which depends only on the
metric and extrinsic curvature induced on the surface. The metric and the
curvature, along with the basis vectors which connect them to the embedding
functions defining the surface, are introduced as auxiliary variables by adding
appropriate constraints, all of them quadratic. The response of the Hamiltonian
to a deformation in each of the variables is examined and the relationship
between the multipliers implementing the constraints and the conserved stress
tensor of the theory established.Comment: 8 page
Conformally invariant bending energy for hypersurfaces
The most general conformally invariant bending energy of a closed
four-dimensional surface, polynomial in the extrinsic curvature and its
derivatives, is constructed. This invariance manifests itself as a set of
constraints on the corresponding stress tensor. If the topology is fixed, there
are three independent polynomial invariants: two of these are the
straighforward quartic analogues of the quadratic Willmore energy for a
two-dimensional surface; one is intrinsic (the Weyl invariant), the other
extrinsic; the third invariant involves a sum of a quadratic in gradients of
the extrinsic curvature -- which is not itself invariant -- and a quartic in
the curvature. The four-dimensional energy quadratic in extrinsic curvature
plays a central role in this construction.Comment: 16 page
The Geometrical Structure of 2d Bond-Orientational Order
We study the formulation of bond-orientational order in an arbitrary two
dimensional geometry. We find that bond-orientational order is properly
formulated within the framework of differential geometry with torsion. The
torsion reflects the intrinsic frustration for two-dimensional crystals with
arbitrary geometry. Within a Debye-Huckel approximation, torsion may be
identified as the density of dislocations. Changes in the geometry of the
system cause a reorganization of the torsion density that preserves
bond-orientational order. As a byproduct, we are able to derive several
identities involving the topology, defect density and geometric invariants such
as Gaussian curvature. The formalism is used to derive the general free energy
for a 2D sample of arbitrary geometry, both in the crystalline and hexatic
phases. Applications to conical and spherical geometries are briefly addressed.Comment: 22 pages, LaTeX, 4 eps figures Published versio
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