107 research outputs found
Large deviations, condensation, and giant response in a statistical system
We study the probability distribution of the sum of a large number of
non-identically distributed random variables . Condensation of
fluctuations, the phenomenon whereby one of such variables provides a
macroscopic contribution to the global probability, is discussed and
interpreted in analogy to phase-transitions in Statistical Mechanics. A general
expression for is derived, and its sensitivity to the details of the
distribution of a single is worked out. These general results are
verified by the analytical and numerical solution of some specific examples.Comment: New improved and extended version (12 pages, 4 figures) with more
references and additional discussions. To appear in J. Phys. A: Math. Theo
Coarsening in inhomogeneous systems
This Article is a brief review of coarsening phenomena occurring in systems
where quenched features - such as random field, varying coupling constants or
lattice vacancies - spoil homogeneity. We discuss the current understanding of
the problem in ferromagnetic systems with a non-conserved scalar order
parameter by focusing primarily on the form of the growth-law of the ordered
domains and on the scaling properties.Comment: 13 pages, 5 figures. This paper is a contribution to the special
issue "Coarsening dynamics", Comptes Rendus de Physique,
https://sites.google.com/site/ppoliti/crp-special-issu
Fast growth at low temperature in vacancy-mediated phase-separation
We study the phase-separation dynamics of a two-dimensional Ising model where
A and B particles can only exchange position with a vacancy. In a wide range of
temperatures the kinetics is dominated, during a long preasymptotic regime, by
diffusion processes of particles along domain interfaces. The dynamical
exponent z associated to this mechanism differs from the one usually expected
for Kawasaki dynamics and is shown to assume different values depending on
temperature and relative AB concentration. At low temperatures, in particular,
domains grow as t^{1/2}, for equal AB volume fractions.Comment: LaTeX, 5 pages, 4 figures, to appear on Phys. Rev.
Condensation of Fluctuations in and out of Equilibrium
Condensation of fluctuations is an interesting phenomenon conceptually
distinct from condensation on average. One stricking feature is that, contrary
to what happens on average, condensation of fluctuations may occurr even in the
absence of interaction. The explanation emerges from the duality between large
deviation events in the given system and typical events in a new and
appropriately biased system. This surprising phenomenon is investigated in the
context of the Gaussian model, chosen as paradigmatical non interacting system,
before and after an istantaneous temperature quench. It is shown that the bias
induces a mean-field-like effective interaction responsible of the condensation
on average. Phase diagrams, covering both the equilibrium and the
off-equilibrium regimes, are derived for observables representative of generic
behaviors.Comment: 8 pages, 7 figure
The role of initial state and final quench temperature on the aging properties in phase-ordering kinetics
We study numerically the two-dimensional Ising model with non-conserved
dynamics quenched from an initial equilibrium state at the temperature to a final temperature below the critical one. By considering
processes initiating both from a disordered state at infinite temperature
and from the critical configurations at and spanning the
range of final temperatures we elucidate the role played by
and on the aging properties and, in particular, on the behavior of
the autocorrelation and of the integrated response function . Our
results show that for any choice of , while the autocorrelation function
exponent takes a markedly different value for
[] or [] the response function exponents are unchanged. Supported by the outcome
of the analytical solution of the solvable spherical model we interpret this
fact as due to the different contributions provided to autocorrelation and
response by the large-scale properties of the system. As changing is
considered, although this is expected to play no role in the
large-scale/long-time properties of the system, we show important effects on
the quantitative behavior of . In particular, data for quenches to
are consistent with a value of the response function exponent different from the one [] found in a wealth of previous numerical determinations
in quenches to finite final temperatures. This is interpreted as due to
important pre-asymptotic corrections associated to .Comment: 25 pages, 15 figures. To appear on Phys. Rev.
Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
We study analytically the distribution of fluctuations of the quantities
whose average yield the usual two-point correlation and linear response
functions in three unfrustrated models: the random walk, the dimensional
scalar field and the 2d XY model. In particular we consider the time dependence
of ratios between composite operators formed with these fluctuating quantities
which generalize the largely studied fluctuation-dissipation ratio, allowing us
to discuss the relevance of the effective temperature notion beyond linear
order. The behavior of fluctuations in the aforementioned solvable cases is
compared to numerical simulations of the 2d clock model with states.Comment: 27 pages, 3 figure
Out of equilibrium dynamics of the spiral model
We study the relaxation of the bi-dimensional kinetically constrained spiral
model. We show that due to the reversibility of the dynamic rules any unblocked
state fully decorrelates in finite times irrespectively of the system being in
the unjammed or the jammed phase. In consequence, the evolution of any
unblocked configuration occurs in a different sector of phase space from the
one that includes the equilibrium blocked equilibrium configurations at
criticality and in the jammed phase. We argue that such out of equilibrium
dynamics share many points in common with coarsening in the one-dimensional
Ising model and we identify the coarsening structures that are, basically,
lines of vacancies. We provide evidence for this claim by analyzing the
behaviour of several observables including the density of particles and
vacancies, the spatial correlation function, the time-dependent persistence and
the linear response.Comment: 14 pages 12 figure
Comment on "Scaling of the linear response in simple aging systems without disorder"
We have repeated the simulations of Henkel, Paessens and Pleimling (HPP)
[Phys.Rev.E {\bf 69}, 056109 (2004)] for the field-cooled susceptibility
in the quench of ferromagnetic systems to
and below . We show that, contrary to the statement made by HPP, the
exponent coincides with the exponent of the linear response function
. We point out what are the assumptions in the
argument of HPP that lead them to the conclusion .Comment: 4 pages, 4 figure
Heat exchanges in coarsening systems
This paper is a contribution to the understanding of the thermal properties
of aging systems where statistically independent degrees of freedom with
largely separated timescales are expected to coexist. Focusing on the
prototypical case of quenched ferromagnets, where fast and slow modes can be
respectively associated to fluctuations in the bulk of the coarsening domains
and to their interfaces, we perform a set of numerical experiments specifically
designed to compute the heat exchanges between different degrees of freedom.
Our studies promote a scenario with fast modes acting as an equilibrium
reservoir to which interfaces may release heat through a mechanism that allows
fast and slow degrees to maintain their statistical properties independent.Comment: 12 pages, 8 figure
On a relation between roughening and coarsening
We argue that a strict relation exists between two in principle unrelated
quantities: The size of the growing domains in a coarsening system, and the
kinetic roughening of an interface. This relation is confirmed by extensive
simulations of the Ising model with different forms of quenched disorder, such
as random bonds, random fields and stochastic dilution.Comment: 8 pages, 3 figures. To appear on EP
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