178 research outputs found
Translation invariant Gibbs states for the Ising model
We prove that all the translation invariant Gibbs states of the Ising model
are a linear combination of the pure phases in the phase
transition regime. This implies that the average magnetization is continuous in
the phase transition regime (). Furthermore, combined with
previous results on the slab percolation threshold this shows the validity of
Pisztora's coarse graining up to the critical temperature.Comment: 14 pages, 3 figure
Quantitative estimates for the flux of TASEP with dilute site disorder
We prove that the flux function of the totally asymmetric simple exclusion
process (TASEP) with site disorder exhibits a flat segment for sufficiently
dilute disorder. For high dilution, we obtain an accurate description of the
flux. The result is established undera decay assumption of the maximum current
in finite boxes, which is implied in particular by a sufficiently slow power
tail assumption on the disorder distribution near its minimum. To circumvent
the absence of explicit invariant measures, we use an original renormalization
procedure and some ideas inspired by homogenization
Winterbottom Construction for Finite Range Ferromagnetic Models: An L_1 Approach
We provide a rigorous microscopic derivation of the thermodynamic description
of equilibrium crystal shapes in the presence of a substrate, first studied by
Winterbottom. We consider finite range ferromagnetic Ising models with pair
interactions in dimensions greater or equal to 3, and model the substrate by a
finite-range boundary magnetic field acting on the spins close to the bottom
wall of the box
Current large deviations in a driven dissipative model
We consider lattice gas diffusive dynamics with creation-annihilation in the
bulk and maintained out of equilibrium by two reservoirs at the boundaries.
This stochastic particle system can be viewed as a toy model for granular gases
where the energy is injected at the boundary and dissipated in the bulk. The
large deviation functional for the particle currents flowing through the system
is computed and some physical consequences are discussed: the mechanism for
local current fluctuations, dynamical phase transitions, the
fluctuation-relation
Lyapunov functionals for boundary-driven nonlinear drift-diffusions
We exhibit a large class of Lyapunov functionals for nonlinear
drift-diffusion equations with non-homogeneous Dirichlet boundary conditions.
These are generalizations of large deviation functionals for underlying
stochastic many-particle systems, the zero range process and the
Ginzburg-Landau dynamics, which we describe briefly. As an application, we
prove linear inequalities between such an entropy-like functional and its
entropy production functional for the boundary-driven porous medium equation in
a bounded domain with positive Dirichlet conditions: this implies exponential
rates of relaxation related to the first Dirichlet eigenvalue of the domain. We
also derive Lyapunov functions for systems of nonlinear diffusion equations,
and for nonlinear Markov processes with non-reversible stationary measures
Vortices in the two-dimensional Simple Exclusion Process
We show that the fluctuations of the partial current in two dimensional
diffusive systems are dominated by vortices leading to a different scaling from
the one predicted by the hydrodynamic large deviation theory. This is supported
by exact computations of the variance of partial current fluctuations for the
symmetric simple exclusion process on general graphs. On a two-dimensional
torus, our exact expressions are compared to the results of numerical
simulations. They confirm the logarithmic dependence on the system size of the
fluctuations of the partialflux. The impact of the vortices on the validity of
the fluctuation relation for partial currents is also discussed.Comment: Revised version to appear in Journal of Statistical Physics. Minor
correction
A diffusive system driven by a battery or by a smoothly varying field
We consider the steady state of a one dimensional diffusive system, such as
the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at
the origin or by a smoothly varying field along the ring. The battery appears
as the limiting case of a smoothly varying field, when the field becomes a
delta function at the origin. We find that in the scaling limit, the long range
pair correlation functions of the system driven by a battery turn out to be
very different from the ones known in the steady state of the SSEP maintained
out of equilibrium by contact with two reservoirs, even when the steady state
density profiles are identical in both models
Current reservoirs in the simple exclusion process
We consider the symmetric simple exclusion process in the interval
with additional birth and death processes respectively on , , and
. The exclusion is speeded up by a factor , births and deaths
by a factor . Assuming propagation of chaos (a property proved in a
companion paper "Truncated correlations in the stirring process with births and
deaths") we prove convergence in the limit to the linear heat
equation with Dirichlet condition on the boundaries; the boundary conditions
however are not known a priori, they are obtained by solving a non linear
equation. The model simulates mass transport with current reservoirs at the
boundaries and the Fourier law is proved to hold
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