Reply to Comment on " Universal Fluctuations in Correlated Systems"
Reply to the comment, cond-mat/0209398 by by N.W. Watkins, S.C. Chapman, and G. Rowlands
cond-mat.stat-mech↗
arXiv subjects
M. Nicodemi
Publications and source records attributed to M. Nicodemi.
Reply to Comment on "Universal Fluctuations in Correlated Systems", by B. Zheng and S. Trimper, cond-mat/0109003
We reply to the comment on our published paper `` Universal Fluctuations in Correlated Systems'',Phys. Rev. Lett. Vol; 84, p3744 (2000), by B. Zheng and S. Trimper, cond-mat/0109003. We argue that their results confirm our conjecture, that the probability distribution for order parameter fluctuations in the 2D and 3D Ising models at a temperature $T^{\ast}(L)$ slightly below $T_C$ for the infinite, system approximates the universal functional form of the 2D-XY model in its low temperature phase. We discuss the relevance of the temperature interval $T_C-T^{\ast}$, considered to be large by Zheng and Trimper and explain why the observed phenomena is a critical phenomena.
cond-mat.stat-mech↗
Vortices Clustering: The Origin of the Second Peak in the Magnetisation Loops of High Temperature Superconductors
We study vortex clustering in type II Superconductors. We demonstrate that the ``second peak'' observed in magnetisation loops may be a dynamical effect associated with a density driven instability of the vortex system. At the microscopic level the instability shows up as the clustering of individual vortices at (rare) preferential regions of the pinning potential. In the limit of quasi-static ramping the instability is related to a phase transition in the equilibrium vortex system.
cond-mat.supr-con↗
Universal Fluctuations in Correlated Systems
The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D-XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated, equilibrium and non-equilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sand-piles, avalanches and granular media in a self organized critical state. We discuss the relationship with both Gaussian and extremal statistics.
cond-mat.stat-mech↗
Scaling properties in off equilibrium dynamical processes
In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations $C(t,t')$. We show, under general conditions, that $C(t,t')$ must obey the following scaling behavior $C(t,t') = ϕ_1(t)^{f(β)}{\cal{S}}(β)$, where the scaling variable is $β=β(ϕ_1(t')/ϕ_1(t))$ and $ϕ_1(t')$, $ϕ_1(t)$ two undetermined functions. The presence of a non constant exponent $f(β)$ signals the appearance of multiscaling properties in the dynamics.
cond-mat↗
Internal avalanches in models of granular media
We study the phenomenon of internal avalanching within the context of recently introduced lattice models of granular media. The avalanche is produced by pulling out a grain at the base of the packing and studying how many grains have to rearrange before the packing is once more stable. We find that the avalanches are long-ranged, decaying as a power-law. We study the distriution of avalanches as a function of the density of the packing and find that the avalanche distribution is a very sensitive structural probe of the system.
cond-mat.stat-mech↗
A ``Tetris''-like model for the Compaction of Dry Granular Media
We propose a two-dimensional geometrical model, based on the concept of geometrical frustration, conceived for the study of compaction in granular media. The dynamics exhibits an interesting inverse logarithmic law that is well known from real experiments. Moreover we present a simple dynamical model of $N$ planes exchanging particles with excluded volume problems, which allows to clarify the origin of the logarithmic relaxations and the stationary density distribution. A simple mapping allows us to cast this Tetris-like model in the form of an Ising-like spin systems with vacancies.
cond-mat↗
Percolation and cluster Monte Carlo dynamics for spin models
A general scheme for devising efficient cluster dynamics proposed in a previous letter [Phys.Rev.Lett. 72, 1541 (1994)] is extensively discussed. In particular the strong connection among equilibrium properties of clusters and dynamic properties as the correlation time for magnetization is emphasized. The general scheme is applied to a number of frustrated spin model and the results discussed.
cond-mat↗