80 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
Can cooperation slow down emergency evacuations?
We study the motion of pedestrians through obscure corridors where the lack
of visibility hides the precise position of the exits. Using a lattice model,
we explore the effects of cooperation on the overall exit flux (evacuation
rate). More precisely, we study the effect of the buddying threshold (of
no--exclusion per site) on the dynamics of the crowd. In some cases, we note
that if the evacuees tend to cooperate and act altruistically, then their
collective action tends to favor the occurrence of disasters.Comment: arXiv admin note: text overlap with arXiv:1203.485
Renormalization Group results for lattice surface models
We study the phase diagram of statistical systems of closed and open
interfaces built on a cubic lattice. Interacting closed interfaces can be
written as Ising models, while open surfaces as Z(2) gauge systems. When the
open surfaces reduce to closed interfaces with few defects, also the gauge
model can be written as an Ising spin model. We apply the lower bound
renormalization group (LBRG) transformation introduced by Kadanoff (Phys. Rev.
Lett. 34, 1005 (1975)) to study the Ising models describing closed and open
surfaces with few defects. In particular, we have studied the Ising-like
transition of self-avoiding surfaces between the random-isotropic phase and the
phase with broken global symmetry at varying values of the mean curvature. Our
results are compared with previous numerical work. The limits of the LBRG
transformation in describing regions of the phase diagram where not
ferromagnetic ground-states are relevant are also discussed.Comment: 24 pages, latex, 5 figures (available upon request to
[email protected]
Finite size scaling in three-dimensional bootstrap percolation
We consider the problem of bootstrap percolation on a three dimensional
lattice and we study its finite size scaling behavior. Bootstrap percolation is
an example of Cellular Automata defined on the -dimensional lattice
in which each site can be empty or occupied by a single
particle; in the starting configuration each site is occupied with probability
, occupied sites remain occupied for ever, while empty sites are occupied by
a particle if at least among their nearest neighbor sites are
occupied. When is fixed, the most interesting case is the one :
this is a sort of threshold, in the sense that the critical probability
for the dynamics on the infinite lattice switches from zero to one
when this limit is crossed. Finite size effects in the three-dimensional case
are already known in the cases : in this paper we discuss the case
and we show that the finite size scaling function for this problem is
of the form . We prove a conjecture proposed by
A.C.D. van Enter.Comment: 18 pages, LaTeX file, no figur
Stationary uphill currents in locally perturbed Zero Range Processes
Uphill currents are observed when mass diffuses in the direction of the
density gradient. We study this phenomenon in stationary conditions in the
framework of locally perturbed 1D Zero Range Processes (ZRP). We show that the
onset of currents flowing from the reservoir with smaller density to the one
with larger density can be caused by a local asymmetry in the hopping rates on
a single site at the center of the lattice. For fixed injection rates at the
boundaries, we prove that a suitable tuning of the asymmetry in the bulk may
induce uphill diffusion at arbitrarily large, finite volumes. We also deduce
heuristically the hydrodynamic behavior of the model and connect the local
asymmetry characterizing the ZRP dynamics to a matching condition relevant for
the macroscopic problem
Compacton formation under Allen--Cahn dynamics
We study the solutions of a generalized Allen-Cahn equation deduced from a
Landau energy functional, endowed with a non-constant higher order stiffness.
We analytically solve the stationary problem and deduce the existence of
so-called compactons, namely, connections on a finite interval between the two
phases. The dynamics problem is numerically solved and compacton formation is
described
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
Stationary currents in particle systems with constrained hopping rates
We study the effect on the stationary currents of constraints affecting the
hopping rates in stochastic particle systems. In the framework of Zero Range
Processes with drift within a finite volume, we discuss how the current is
reduced by the presence of the constraint and deduce exact formulae, fully
explicit in some cases. The model discussed here has been introduced in Ref.
[1] and is relevant for the description of pedestrian motion in elongated dark
corridors, where the constraint on the hopping rates can be related to
limitations on the interaction distance among pedestrians
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