Related papers: Local scale-invariance in disordered systems
Dynamics of spin-glasses subjected to slow continuous changes of working enviroment such as slow changes of temperature or interaction bonds are studied based on scaling arguments and numerical simulations of continuous bond changes. Such…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local…
The local scale invariance has been investigated in the nonequilibrium kinetic Ising model exhibiting absorbing phase transition of PC type in 1+1 dimension. Numerical evidence has been found for the satisfaction of this symmetry and…
Nonequilibrium surface autocorrelation and autoresponse functions are studied numerically in semi-infinite critical systems in the dynamical scaling regime. Dynamical critical behaviour is examined for a nonconserved order parameter in…
Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local…
We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a…
This lecture deals with glassy dynamics and aging in disordered systems. Special emphasis is put on dynamic mean field theory. In the first part I present some of the systems of interest, in particular spin-glasses, supercooled liquids and…
We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations…
We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not…
The non-equilibrium dynamics of three paradigmatic models for two-dimensional systems with quenched disorder is studied with a focus on the existence and analysis of a growing length scale during aging at low temperatures: 1) The random…
We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the non-diluted…
The ageing of the bond-disordered two-dimensional Ising model quenched to below its critical point is studied through the two-time autocorrelator and thermoremanent magnetization (TRM). The corresponding ageing exponents are determined. The…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
We investigate numerically disorder chaos in spin glasses, i.e. the sensitivity of the ground state to small changes of the random couplings. Our study focuses on the Edwards-Anderson model in d=1,2,3 and in mean-field. We find that in all…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched…