2,862 research outputs found
Renormalization-group at criticality and complete analyticity of constrained models: a numerical study
We study the majority rule transformation applied to the Gibbs measure for
the 2--D Ising model at the critical point. The aim is to show that the
renormalized hamiltonian is well defined in the sense that the renormalized
measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman Uniqueness
(DSU) finite-size condition for the "constrained models" corresponding to
different configurations of the "image" system. It is known that DSU implies,
in our 2--D case, complete analyticity from which, as it has been recently
shown by Haller and Kennedy, Gibbsianness follows. We introduce a Monte Carlo
algorithm to compute an upper bound to Vasserstein distance (appearing in DSU)
between finite volume Gibbs measures with different boundary conditions. We get
strong numerical evidence that indeed DSU condition is verified for a large
enough volume for all constrained models.Comment: 39 pages, teX file, 4 Postscript figures, 1 TeX figur
Linear Boltzmann dynamics in a strip with large reflective obstacles: stationary state and residence time
The presence of obstacles modify the way in which particles diffuse. In
cells, for instance, it is observed that, due to the presence of macromolecules
playing the role of obstacles, the mean square displacement ofbiomolecules
scales as a power law with exponent smaller than one. On the other hand,
different situations in grain and pedestrian dynamics in which the presence of
an obstacle accelerate the dynamics are known. We focus on the time, called
residence time, needed by particles to cross a strip assuming that the dynamics
inside the strip follows the linear Boltzmann dynamics. We find that the
residence time is not monotonic with the sizeand the location of the obstacles,
since the obstacle can force those particles that eventually cross the strip to
spend a smaller time in the strip itself. We focus on the case of a rectangular
strip with two open sides and two reflective sides and we consider reflective
obstaclea into the strip
Metastability for reversible probabilistic cellular automata with self--interaction
The problem of metastability for a stochastic dynamics with a parallel
updating rule is addressed in the Freidlin--Wentzel regime, namely, finite
volume, small magnetic field, and small temperature. The model is characterized
by the existence of many fixed points and cyclic pairs of the zero temperature
dynamics, in which the system can be trapped in its way to the stable phase.
%The characterization of the metastable behavior %of a system in the context of
parallel dynamics is a very difficult task, %since all the jumps in the
configuration space are allowed. Our strategy is based on recent powerful
approaches, not needing a complete description of the fixed points of the
dynamics, but relying on few model dependent results. We compute the exit time,
in the sense of logarithmic equivalence, and characterize the critical droplet
that is necessarily visited by the system during its excursion from the
metastable to the stable state. We need to supply two model dependent inputs:
(1) the communication energy, that is the minimal energy barrier that the
system must overcome to reach the stable state starting from the metastable
one; (2) a recurrence property stating that for any configuration different
from the metastable state there exists a path, starting from such a
configuration and reaching a lower energy state, such that its maximal energy
is lower than the communication energy
Sum of exit times in series of metastable states in probabilistic cellular automata
Reversible Probabilistic Cellular Automata are a special class
of automata whose stationary behavior is described by Gibbs--like
measures. For those models the dynamics can be trapped for a very
long time in states which are very different from the ones typical
of stationarity.
This phenomenon can be recasted in the framework of metastability
theory which is typical of Statistical Mechanics.
In this paper we consider a model presenting two not degenerate in
energy
metastable states which form a series, in the sense that,
when the dynamics is started at one of them, before reaching
stationarity, the system must necessarily visit the second one.
We discuss a rule for combining the exit times
from each of the metastable states
Metastability in the two-dimensional Ising model with free boundary conditions
We investigate metastability in the two dimensional Ising model in a square
with free boundary conditions at low temperatures. Starting with all spins down
in a small positive magnetic field, we show that the exit from this metastable
phase occurs via the nucleation of a critical droplet in one of the four
corners of the system. We compute the lifetime of the metastable phase
analytically in the limit , and via Monte Carlo simulations at
fixed values of and and find good agreement. This system models the
effects of boundary domains in magnetic storage systems exiting from a
metastable phase when a small external field is applied.Comment: 24 pages, TeX fil
A combinatorial proof of tree decay of semi-invariants
We consider finite range Gibbs fields and provide a purely combinatorial
proof of the exponential tree decay of semi--invariants, supposing that the
logarithm of the partition function can be expressed as a sum of suitable local
functions of the boundary conditions. This hypothesis holds for completely
analytical Gibbs fields; in this context the tree decay of semi--invariants has
been proven via analyticity arguments. However the combinatorial proof given
here can be applied also to the more complicated case of disordered systems in
the so called Griffiths' phase when analyticity arguments fail
A model for enhanced and selective transport through biological membranes with alternating pores
We investigate the outflux of ions through the channels in a cell membrane.
The channels undergo an open/close cycle according to a periodic schedule. Our
study is based both on theoretical considerations relying on homogenization
theory, and on Monte Carlo numerical simulations. We examine the onset of a
limiting boundary behavior characterized by a constant ratio between the
outflux and the local density, in the thermodynamics limit. The focus here is
on the issue of selectivity, that is on the different behavior of the ion
currents through the channel in the cases of the selected and non-selected
species.Comment: arXiv admin note: text overlap with arXiv:1307.418
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