236 research outputs found
Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets
We present comprehensive numerical results for domain growth in the
two-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauber
kinetics. We characterize the evolution via the {\it domain growth law}, and
two-time quantities like the {\it autocorrelation function} and {\it
autoresponse function}. Our results clearly establish that the growth law shows
a crossover from a pre-asymptotic regime with "power-law growth with a
disorder-dependent exponent" to an asymptotic regime with "logarithmic growth".
We compare this behavior with previous results on one-dimensional disordered
systems and we propose a unifying picture in a renormalization group framework.
We also study the corresponding crossover in the scaling functions for the
two-time quantities. Super-universality is found not to hold. Clear evidence
supporting the dimensionality dependence of the scaling exponent of the
autoresponse function is obtained.Comment: Thoroughly revised manuscript. The Introduction, Section 2 and
Section 4 have been largely rewritten. References added. Final version
accepted for publication on Journal of Statistical Mechanics: Theory and
Experimen
Nonlinear susceptibilities and the measurement of a cooperative length
We derive the exact beyond-linear fluctuation dissipation relation,
connecting the response of a generic observable to the appropriate correlation
functions, for Markov systems. The relation, which takes a similar form for
systems governed by a master equation or by a Langevin equation, can be derived
to every order, in large generality with respect to the considered model, in
equilibrium and out of equilibrium as well. On the basis of the fluctuation
dissipation relation we propose a particular response function, namely the
second order susceptibility of the two-particle correlation function, as an
effective quantity to detect and quantify cooperative effects in glasses and
disordered systems. We test this idea by numerical simulations of the
Edwards-Anderson model in one and two dimensions.Comment: 5 pages, 2 figure
Interface fluctuations, bulk fluctuations and dimensionality in the off-equilibrium response of coarsening systems
The relationship between statics and dynamics proposed by Franz, Mezard,
Parisi and Peliti (FMPP) for slowly relaxing systems [Phys.Rev.Lett. {\bf 81},
1758 (1998)] is investigated in the framework of non disordered coarsening
systems. Separating the bulk from interface response we find that for statics
to be retrievable from dynamics the interface contribution must be
asymptotically negligible. How fast this happens depends on dimensionality.
There exists a critical dimensionality above which the interface response
vanishes like the interface density and below which it vanishes more slowly. At
the interface response does not vanish leading to the violation of the
FMPP scheme. This behavior is explained in terms of the competition between
curvature driven and field driven interface motion.Comment: 11 pages, 3 figures. Significantly improved version of the paper with
new results, new numerical simulations and new figure
Memory in Self Organized Criticality
Many natural phenomena exhibit power law behaviour in the distribution of
event size. This scaling is successfully reproduced by Self Organized
Criticality (SOC). On the other hand, temporal occurrence in SOC models has a
Poisson-like statistics, i.e. exponential behaviour in the inter-event time
distribution, in contrast with experimental observations. We present a SOC
model with memory: events are nucleated not only as a consequence of the
instantaneous value of the local field with respect to the firing threshold,
but on the basis of the whole history of the system. The model is able to
reproduce the complex behaviour of inter-event time distribution, in excellent
agreement with experimental seismic data
Scaling and universality in the aging kinetics of the two-dimensional clock model
We study numerically the aging dynamics of the two-dimensional p-state clock
model after a quench from an infinite temperature to the ferromagnetic phase or
to the Kosterlitz-Thouless phase. The system exhibits the general scaling
behavior characteristic of non-disordered coarsening systems. For quenches to
the ferromagnetic phase, the value of the dynamical exponents, suggests that
the model belongs to the Ising-type universality class. Specifically, for the
integrated response function , we find
consistent with the value found in the two-dimensional
Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures
Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
We study the nonconserved phase ordering dynamics of the d = 2, 3 random
field Ising model, quenched to below the critical temperature. Motivated by the
puzzling results of previous work in two and three di- mensions, reporting a
crossover from power-law to logarithmic growth, together with superuniversal
behavior of the correlation function, we have undertaken a careful
investigation of both the domain growth law and the autocorrelation function.
Our main results are as follows: We confirm the crossover to asymptotic
logarithmic behavior in the growth law, but, at variance with previous
findings, the exponent in the preasymptotic power law is disorder-dependent,
rather than being the one of the pure system. Furthermore, we find that the
autocorre- lation function does not display superuniversal behavior. This
restores consistency with previous results for the d = 1 system, and fits
nicely into the unifying scaling scheme we have recently proposed in the study
of the random bond Ising model.Comment: To be published in Physical Review
Slow relaxation in the large N model for phase ordering
The basic features of the slow relaxation phenomenology arising in phase
ordering processes are obtained analytically in the large model through the
exact separation of the order parameter into the sum of thermal and
condensation components. The aging contribution in the response function
is found to obey a pattern of behavior, under variation of
dimensionality, qualitatively similar to the one observed in Ising systems.
There exists a critical dimensionality above which
is proportional to the defect density , while for it vanishes
more slowly than and at does not vanish. As in the Ising
case, this behavior can be understood in terms of the dependence on
dimensionality of the interplay between the defect density and the effective
response associated to a single defect.Comment: 27 pages, 4 figures, accepted for publication on Phys.Rev.
The daily life of a researcher introduced with an online data analysis experience based on visual programming
A common criticism for the Italian higher education system is the gap that separates it from the employment landscape. To improve this situation, our department and schools are sponsoring internships, to expose the students to the work life. Groups of two high school students are invited to work with researchers for a week. A tutor introduces them to the research theme and proposes related activities. In order not to require previous experience with programming languages, the visual programming language Blockly is used as the development toolkit, for its suitability for educational activities. We present the development of new functionalities for Blockly purposely for the project: online reading data from a real detection system, interactive analysis, and online data visualization. The activity was successfully experienced by the students hosted in the research group. The actual implementation of the analysis algorithm was quickly achieved, even with no prior experience with data analysis. We bypassed the difficulties related to the syntax of programming languages, by employing Blockly and our added features; this allowed us to focus on the fundamental concepts. The students enjoyed the whole experience and were very proactive asking relevant questions and proposing ideas
Scaling Behavior of Response Functions in the Coarsening Dynamics of Disordered Ferromagnets
We study coarsening dynamics in the ferromagnetic random bond Ising model in
d = 1; 2. We focus on the validity of super-universality and the scaling
properties of the response functions. In the d = 1 case, we obtain a complete
understanding of the evolution, from pre- asymptotic to asymptotic behavior.
The corresponding response function shows a clear violation of
super-universality. Further, our results for d = 1; 2 settle the controversy
regarding the decay exponent which characterizes the response function
Nonlinear response and fluctuation dissipation relations
A unified derivation of the off equilibrium fluctuation dissipation relations
(FDR) is given for Ising and continous spins to arbitrary order, within the
framework of Markovian stochastic dynamics. Knowledge of the FDR allows to
develop zero field algorithms for the efficient numerical computation of the
response functions. Two applications are presented. In the first one, the
problem of probing for the existence of a growing cooperative length scale is
considered in those cases, like in glassy systems, where the linear FDR is of
no use. The effectiveness of an appropriate second order FDR is illustrated in
the test case of the Edwards-Anderson spin glass in one and two dimensions. In
the second one, the important problem of the definition of an off equilibrium
effective temperature through the nonlinear FDR is considered. It is shown
that, in the case of coarsening systems, the effective temperature derived from
the second order FDR is consistent with the one obtained from the linear FDR.Comment: 24 pages, 6 figure
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