559 research outputs found
Quadri-tilings of the plane
We introduce {\em quadri-tilings} and show that they are in bijection with
dimer models on a {\em family} of graphs arising from rhombus
tilings. Using two height functions, we interpret a sub-family of all
quadri-tilings, called {\em triangular quadri-tilings}, as an interface model
in dimension 2+2. Assigning "critical" weights to edges of , we prove an
explicit expression, only depending on the local geometry of the graph ,
for the minimal free energy per fundamental domain Gibbs measure; this solves a
conjecture of \cite{Kenyon1}. We also show that when edges of are
asymptotically far apart, the probability of their occurrence only depends on
this set of edges. Finally, we give an expression for a Gibbs measure on the
set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs
measures, and conjecture it to be that of minimal free energy per fundamental
domain.Comment: Revised version, minor changes. 30 pages, 13 figure
Flux Creep and Flux Jumping
We consider the flux jump instability of the Bean's critical state arising in
the flux creep regime in type-II superconductors. We find the flux jump field,
, that determines the superconducting state stability criterion. We
calculate the dependence of on the external magnetic field ramp rate,
. We demonstrate that under the conditions typical for most of the
magnetization experiments the slope of the current-voltage curve in the flux
creep regime determines the stability of the Bean's critical state, {\it i.e.},
the value of . We show that a flux jump can be preceded by the
magneto-thermal oscillations and find the frequency of these oscillations as a
function of .Comment: 7 pages, ReVTeX, 2 figures attached as postscript file
Can we Determine Electric Fields and Poynting Fluxes from Vector Magnetograms and Doppler Measurements?
The availability of vector magnetogram sequences with sufficient accuracy and
cadence to estimate the time derivative of the magnetic field allows us to use
Faraday's law to find an approximate solution for the electric field in the
photosphere, using a Poloidal-Toroidal Decomposition (PTD) of the magnetic
field and its partial time derivative. Without additional information, however,
the electric field found from this technique is under-determined -- Faraday's
law provides no information about the electric field that can be derived the
gradient of a scalar potential. Here, we show how additional information in the
form of line-of-sight Doppler flow measurements, and motions transverse to the
line-of-sight determined with ad-hoc methods such as local correlation
tracking, can be combined with the PTD solutions to provide much more accurate
solutions for the solar electric field, and therefore the Poynting flux of
electromagnetic energy in the solar photosphere. Reliable, accurate maps of the
Poynting flux are essential for quantitative studies of the buildup of magnetic
energy before flares and coronal mass ejections.Comment: Solar Physics, in press. 14 pages, 3 figure
Parametric pumping at finite frequency
We report on a first principles theory for analyzing the parametric electron
pump at a finite frequency. The pump is controlled by two pumping parameters
with phase difference . In the zero frequency limit, our theory predicts
the well known result that the pumped current is proportional to .
For the more general situation of a finite frequency, our theory predicts a
non-vanishing pumped current even when the two driving forces are in phase, in
agreement with the recent experimental results. We present the physical
mechanism behind the nonzero pumped current at , which we found to be
due to photon-assisted processes
Applicability of the Fisher Equation to Bacterial Population Dynamics
The applicability of the Fisher equation, which combines diffusion with
logistic nonlinearity, to population dynamics of bacterial colonies is studied
with the help of explicit analytic solutions for the spatial distribution of a
stationary bacterial population under a static mask. The mask protects the
bacteria from ultraviolet light. The solution, which is in terms of Jacobian
elliptic functions, is used to provide a practical prescription to extract
Fisher equation parameters from observations and to decide on the validity of
the Fisher equation.Comment: 5 pages, 3 figs. include
Kosterlitz Thouless Universality in Dimer Models
Using the monomer-dimer representation of strongly coupled U(N) lattice gauge
theories with staggered fermions, we study finite temperature chiral phase
transitions in (2+1) dimensions. A new cluster algorithm allows us to compute
monomer-monomer and dimer-dimer correlations at zero monomer density (chiral
limit) accurately on large lattices. This makes it possible to show
convincingly, for the first time, that these models undergo a finite
temperature phase transition which belongs to the Kosterlitz-Thouless
universality class. We find that this universality class is unaffected even in
the large N limit. This shows that the mean field analysis often used in this
limit breaks down in the critical region.Comment: 4 pages, 4 figure
Asymptotic Expansions for lambda_d of the Dimer and Monomer-Dimer Problems
In the past few years we have derived asymptotic expansions for lambda_d of
the dimer problem and lambda_d(p) of the monomer-dimer problem. The many
expansions so far computed are collected herein. We shine a light on results in
two dimensions inspired by the work of M. E. Fisher. Much of the work reported
here was joint with Shmuel Friedland.Comment: 4 page
The Electron Spectral Function in Two-Dimensional Fractionalized Phases
We study the electron spectral function of various zero-temperature
spin-charge separated phases in two dimensions. In these phases, the electron
is not a fundamental excitation of the system, but rather ``decays'' into a
spin-1/2 chargeless fermion (the spinon) and a spinless charge e boson (the
chargon). Using low-energy effective theories for the spinons (d-wave pairing
plus possible N\'{e}el order), and the chargons (condensed or quantum
disordered bosons), we explore three phases of possible relevance to the
cuprate superconductors: 1) AF*, a fractionalized antiferromagnet where the
spinons are paired into a state with long-ranged N\'{e}el order and the
chargons are 1/2-filled and (Mott) insulating, 2) the nodal liquid, a
fractionalized insulator where the spinons are d-wave paired and the chargons
are uncondensed, and 3) the d-wave superconductor, where the chargons are
condensed and the spinons retain a d-wave gap. Working within the gauge
theory of such fractionalized phases, our results should be valid at scales
below the vison gap. However, on a phenomenological level, our results should
apply to any spin-charge separated system where the excitations have these
low-energy effective forms. Comparison with ARPES data in the undoped,
pseudogapped, and superconducting regions is made.Comment: 10 page
Percolation in random environment
We consider bond percolation on the square lattice with perfectly correlated
random probabilities. According to scaling considerations, mapping to a random
walk problem and the results of Monte Carlo simulations the critical behavior
of the system with varying degree of disorder is governed by new, random fixed
points with anisotropic scaling properties. For weaker disorder both the
magnetization and the anisotropy exponents are non-universal, whereas for
strong enough disorder the system scales into an {\it infinite randomness fixed
point} in which the critical exponents are exactly known.Comment: 8 pages, 7 figure
Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder
We study the statistics of thermodynamic quantities in two related systems
with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in
a random potential and the 2-dimensional random bond dimer model. The first
system is examined by a replica-symmetric Bethe ansatz (RBA) while the latter
is studied numerically by a polynomial algorithm which circumvents slow glassy
dynamics. We establish a mapping of the two models which allows for a detailed
comparison of RBA predictions and simulations. Over a wide range of disorder
strength, the effective lattice stiffness and cumulants of various
thermodynamic quantities in both approaches are found to agree excellently. Our
comparison provides, for the first time, a detailed quantitative confirmation
of the replica approach and renders the planar line lattice a unique testing
ground for concepts in random systems.Comment: 16 pages, 14 figure
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