271 research outputs found
On the entanglement entropy for a XY spin chain
The entanglement entropy for the ground state of a XY spin chain is related
to the corner transfer matrices of the triangular Ising model and expressed in
closed form.Comment: 4 pages, 2 figure
Wave-train induced unpinning of weakly anchored vortices in excitable media
A free vortex in excitable media can be displaced and removed by a
wave-train. However, simple physical arguments suggest that vortices anchored
to large inexcitable obstacles cannot be removed similarly. We show that
unpinning of vortices attached to obstacles smaller than the core radius of the
free vortex is possible through pacing. The wave-train frequency necessary for
unpinning increases with the obstacle size and we present a geometric
explanation of this dependence. Our model-independent results suggest that
decreasing excitability of the medium can facilitate pacing-induced removal of
vortices in cardiac tissue.Comment: Published versio
Dynamics of lattice spins as a model of arrhythmia
We consider evolution of initial disturbances in spatially extended systems
with autonomous rhythmic activity, such as the heart. We consider the case when
the activity is stable with respect to very smooth (changing little across the
medium) disturbances and construct lattice models for description of
not-so-smooth disturbances, in particular, topological defects; these models
are modifications of the diffusive XY model. We find that when the activity on
each lattice site is very rigid in maintaining its form, the topological
defects - vortices or spirals - nucleate a transition to a disordered,
turbulent state.Comment: 17 pages, revtex, 3 figure
Ordering in Two-Dimensional Ising Models with Competing Interactions
We study the 2D Ising model on a square lattice with additional non-equal
diagonal next-nearest neighbor interactions. The cases of classical and quantum
(transverse) models are considered. Possible phases and their locations in the
space of three Ising couplings are analyzed. In particular, incommensurate
phases occurring only at non-equal diagonal couplings, are predicted. We also
analyze a spin-pseudospin model comprised of the quantum Ising model coupled to
XY spin chains in a particular region of interactions, corresponding to the
Ising sector's super-antiferromagnetic (SAF) ground state. The spin-SAF
transition in the coupled Ising-XY model into a phase with co-existent SAF
Ising (pseudospin) long-range order and a spin gap is considered. Along with
destruction of the quantum critical point of the Ising sector, the phase digram
of the Ising-XY model can also demonstrate a re-entrance of the spin-SAF phase.
A detailed study of the latter is presented. The mechanism of the re-entrance,
due to interplay of interactions in the coupled model, and the conditions of
its appearance are established. Applications of the spin-SAF theory for the
transition in the quarter-filled ladder compound NaV2O5 are discussed.Comment: Minor revisions and refs. added; published version of the invited
paper in a special issue of "Low Temp. Physics
Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications
In a weakly excitable medium, characterized by a large threshold stimulus,
the free end of an isolated broken plane wave (wave tip) can either rotate
(steadily or unsteadily) around a large excitable core, thereby producing a
spiral pattern, or retract causing the wave to vanish at boundaries. An
asymptotic analysis of spiral motion and retraction is carried out in this
weakly excitable large core regime starting from the free-boundary limit of the
reaction-diffusion models, valid when the excited region is delimited by a thin
interface. The wave description is shown to naturally split between the tip
region and a far region that are smoothly matched on an intermediate scale.
This separation allows us to rigorously derive an equation of motion for the
wave tip, with the large scale motion of the spiral wavefront slaved to the
tip. This kinematic description provides both a physical picture and exact
predictions for a wide range of wave behavior, including: (i) steady rotation
(frequency and core radius), (ii) exact treatment of the meandering instability
in the free-boundary limit with the prediction that the frequency of unstable
motion is half the primary steady frequency (iii) drift under external actions
(external field with application to axisymmetric scroll ring motion in
three-dimensions, and spatial or/and time-dependent variation of excitability),
and (iv) the dynamics of multi-armed spiral waves with the new prediction that
steadily rotating waves with two or more arms are linearly unstable. Numerical
simulations of FitzHug-Nagumo kinetics are used to test several aspects of our
results. In addition, we discuss the semi-quantitative extension of this theory
to finite cores and pinpoint mathematical subtleties related to the thin
interface limit of singly diffusive reaction-diffusion models
Classification of phase transitions and ensemble inequivalence, in systems with long range interactions
Systems with long range interactions in general are not additive, which can
lead to an inequivalence of the microcanonical and canonical ensembles. The
microcanonical ensemble may show richer behavior than the canonical one,
including negative specific heats and other non-common behaviors. We propose a
classification of microcanonical phase transitions, of their link to canonical
ones, and of the possible situations of ensemble inequivalence. We discuss
previously observed phase transitions and inequivalence in self-gravitating,
two-dimensional fluid dynamics and non-neutral plasmas. We note a number of
generic situations that have not yet been observed in such systems.Comment: 42 pages, 11 figures. Accepted in Journal of Statistical Physics.
Final versio
Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states
Scroll waves are three-dimensional analogs of spiral waves. The linear
stability spectrum of untwisted and twisted scroll waves is computed for a
two-variable reaction-diffusion model of an excitable medium. Different bands
of modes are seen to be unstable in different regions of parameter space. The
corresponding bifurcations and bifurcated states are characterized by
performing direct numerical simulations. In addition, computations of the
adjoint linear stability operator eigenmodes are also performed and serve to
obtain a number of matrix elements characterizing the long-wavelength
deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.
Analysis of a three-component model phase diagram by Catastrophe Theory
We analyze the thermodynamical potential of a lattice gas model with three
components and five parameters using the methods of Catastrophe Theory. We find
the highest singularity, which has codimension five, and establish its
transversality. Hence the corresponding seven-degree Landau potential, the
canonical form Wigwam or , constitutes the adequate starting point to
study the overall phase diagram of this model.Comment: 16 pages, Latex file, submitted to Phys. Rev.
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