37 research outputs found
Driven Diffusive Systems: An Introduction and Recent Developments
Nonequilibrium steady states in driven diffusive systems exhibit many
features which are surprising or counterintuitive, given our experience with
equilibrium systems. We introduce the prototype model and review its unusual
behavior in different temperature regimes, from both a simulational and
analytic view point. We then present some recent work, focusing on the phase
diagrams of driven bi-layer systems and two-species lattice gases. Several
unresolved puzzles are posed.Comment: 25 pages, 5 figures, to appear in Physics Reports vol. 299, June 199
Long Range Correlations in the Disordered Phase of a Simple Three State Lattice Gas
We investigate the dynamics of a three-state stochastic lattice gas,
consisting of holes and two oppositely "charged" species of particles, under
the influence of an "electric" field, at zero total charge. Interacting only
through an excluded volume constraint, particles can hop to nearest neighbour
empty sites. With increasing density and drive, the system orders into a
charge-segregated state. Using a combination of Langevin equations and Monte
Carlo simulations, we study the steady-state structure factors in the
disordered phase where homogeneous configurations are stable against small
harmonic perturbations. They show a discontinuity singularity at the origin
which in real space leads to an intricate crossover between power laws of
different kinds.Comment: 7 RevTeX pages, 1 postscript figure include
Possible Existence of an Extraordinary Phase in the Driven Lattice Gas
We report recent simulation results which might indicate the existence of a
new low-temperature "phase" in an Ising lattice gas, driven into a
non-equilibrium steady state by an external field. It appears that this
"phase", characterized by multiple-strip configurations, is selected when
square systems are used to approach the thermodynamic limit. We propose a
quantitative criterion for the existence of such a "phase". If confirmed, its
observation may resolve a long-standing controversy over the critical
properties of the driven Ising lattice gas.Comment: 10 pages; 4 figure
Nematic Films and Radially Anisotropic Delaunay Surfaces
We develop a theory of axisymmetric surfaces minimizing a combination of
surface tension and nematic elastic energies which may be suitable for
describing simple film and bubble shapes. As a function of the elastic constant
and the applied tension on the bubbles, we find the analogues of the unduloid,
sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure
Ordering dynamics of the driven lattice gas model
The evolution of a two-dimensional driven lattice-gas model is studied on an
L_x X L_y lattice. Scaling arguments and extensive numerical simulations are
used to show that starting from random initial configuration the model evolves
via two stages: (a) an early stage in which alternating stripes of particles
and vacancies are formed along the direction y of the driving field, and (b) a
stripe coarsening stage, in which the number of stripes is reduced and their
average width increases. The number of stripes formed at the end of the first
stage is shown to be a function of L_x/L_y^\phi, with \phi ~ 0.2. Thus,
depending on this parameter, the resulting state could be either single or
multi striped. In the second, stripe coarsening stage, the coarsening time is
found to be proportional to L_y, becoming infinitely long in the thermodynamic
limit. This implies that the multi striped state is thermodynamically stable.
The results put previous studies of the model in a more general framework
Continuum theory of vacancy-mediated diffusion
We present and solve a continuum theory of vacancy-mediated diffusion (as
evidenced, for example, in the vacancy driven motion of tracers in crystals).
Results are obtained for all spatial dimensions, and reveal the strongly
non-gaussian nature of the tracer fluctuations. In integer dimensions, our
results are in complete agreement with those from previous exact lattice
calculations. We also extend our model to describe the vacancy-driven
fluctuations of a slaved flux line.Comment: 25 Latex pages, subm. to Physical Review
Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
When Lenz proposed a simple model for phase transitions in magnetism, he
couldn't have imagined that the "Ising model" was to become a jewel in field of
equilibrium statistical mechanics. Its role spans the spectrum, from a good
pedagogical example to a universality class in critical phenomena. A quarter
century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing
a seemingly trivial modification to the Ising lattice gas, they took it into
the vast realms of non-equilibrium statistical mechanics. An abundant variety
of unexpected behavior emerged and caught many of us by surprise. We present a
brief review of some of the new insights garnered and some of the outstanding
puzzles, as well as speculate on the model's role in the future of
non-equilibrium statistical physics.Comment: 3 figures. Proceedings of 100th Statistical Mechanics Meeting,
Rutgers, NJ (December, 2008
Analysis of a three-component model phase diagram by Catastrophe Theory: Potentials with two Order Parameters
In this work we classify the singularities obtained from the Gibbs potential
of a lattice gas model with three components, two order parameters and five
control parameters applying the general theorems provided by Catastrophe
Theory. In particular, we clearly establish the existence of Landau potentials
in two variables or, in other words, corank 2 canonical forms that are
associated to the hyperbolic umbilic, D_{+4}, its dual the elliptic umbilic,
D_{-4}, and the parabolic umbilic, D_5, catastrophes. The transversality of the
potential with two order parameters is explicitely shown for each case. Thus we
complete the Catastrophe Theory analysis of the three-component lattice model,
initiated in a previous paper.Comment: 17 pages, 3 EPS figures, Latex file, continuation of Phys. Rev. B57,
13527 (1998) (cond-mat/9707015), submitted to Phys. Rev.
Decay of the metastable phase in d=1 and d=2 Ising models
We calculate perturbatively the tunneling decay rate of the
metastable phase in the quantum d=1 Ising model in a skew magnetic field near
the coexistence line at T=0. It is shown that
oscillates in the magnetic field due to discreteness of the excitation
energy spectrum. After mapping of the obtained results onto the extreme
anisotropic d=2 Ising model at , we verify in the latter model the
droplet theory predictions for the free energy analytically continued to the
metastable phase. We find also evidence for the discrete-lattice corrections in
this metastable phase free energy.Comment: 4 pages, REVTe
Ultra-Slow Vacancy-Mediated Tracer Diffusion in Two Dimensions: The Einstein Relation Verified
We study the dynamics of a charged tracer particle (TP) on a two-dimensional
lattice all sites of which except one (a vacancy) are filled with identical
neutral, hard-core particles. The particles move randomly by exchanging their
positions with the vacancy, subject to the hard-core exclusion. In case when
the charged TP experiences a bias due to external electric field ,
(which favors its jumps in the preferential direction), we determine exactly
the limiting probability distribution of the TP position in terms of
appropriate scaling variables and the leading large-N ( being the discrete
time) behavior of the TP mean displacement ; the latter is
shown to obey an anomalous, logarithmic law . On comparing our results with earlier predictions by Brummelhuis
and Hilhorst (J. Stat. Phys. {\bf 53}, 249 (1988)) for the TP diffusivity
in the unbiased case, we infer that the Einstein relation
between the TP diffusivity and the mobility holds in the leading in order, despite
the fact that both and are not constant but vanish as . We also generalize our approach to the situation with very small but
finite vacancy concentration , in which case we find a ballistic-type law
. We demonstrate that here,
again, both and , calculated in the linear in
approximation, do obey the Einstein relation.Comment: 25 pages, one figure, TeX, submitted to J. Stat. Phy