A theoretical perspective is provided on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations in studying and understanding the dynamics of systems close to the glass transition at the molecular level is given. The recent progress on the subject of the spatially heterogeneous dynamics that characterizes structural relaxation in materials with slow dynamics is reviewed. The main theoretical approaches are presented describing the glass transition in supercooled liquids, focusing on theories that have a microscopic, statistical mechanics basis. We describe both successes and failures and critically assess the current status of each of these approaches. The physics of aging dynamics in disordered materials and the rheology of soft glassy materials are then discussed, and recent theoretical progress is described. For each section, an extensive overview is given of the most recent advances, but we also describe in some detail the important open problems that will occupy a central place in this field in the coming years.

Theoretical perspective on the glass transition and amorphous materials

TOPICAL REVIEW: Supermagnetism

The magnetic properties of ultra-small (3 nm) CoFe2O4 nanoparticles have been investigated by DC magnetization measurements as a function of temperature and magnetic field. The main features of the magnetic behaviour are blocking of non-interacting particle moments (zero-field-cooled magnetization Tmax≈40 K), a rapid increase of saturation magnetization (up to values higher than for the bulk material) at low T and an increase in anisotropy below 30 K due to the appearance of exchange bias. The low temperature behaviour is determined by a random freezing of surface spins. Localized spin-canting and cation distribution between the two sublattices of the spinel structure account quantitatively for the observed increase in saturation magnetization.

Spin-glass-like freezing and enhanced magnetization in ultra-small CoFe2O4 nanoparticles

We argue that for generic systems close to a critical point, an extended fluctuation-dissipation relation connects the low frequency nonlinear cubic susceptibility to the four-point correlation function. In glassy systems, the latter contains interesting information on the heterogeneity and cooperativity of the dynamics. Our result suggests that if the abrupt slowing down of glassy materials is indeed accompanied by the growth of a cooperative length , then the nonlinear, 3 response to an oscillating field at frequency should substantially increase and give direct information on the temperature or density dependence of . The analysis of the nonlinear compressibility or the dielectric susceptibility in supercooled liquids, or the nonlinear magnetic susceptibility in spin-glasses, should give access to a cooperative length scale, that grows as the temperature is decreased or as the age of the system increases. Our theoretical analysis holds exactly within the modecoupling theory of glasses.

Nonlinear susceptibility in glassy systems: A probe for cooperative dynamical length scales

In this introductory talk, we shall present spin glasses and review the general experimental features of their glassy dynamics [1]. Spin glasses are model magnetic systems in which the interactions are disordered and frustrated, due to a random dilution of magnetic ions. Below their glass temperature Tg , their response to a magnetic excitation is a slow relaxation of the magnetization, which strongly depends on the time spent below Tg (« aging » phenomenon). In contrast with structural and polymer glasses, aging is here hardly influenced by the cooling rate. During cooling, each further step down tends to restart some aging processes (« rejuvenation »), while the memory of previous aging periods, achieved at different temperatures during cooling, can be retrieved when re-heating [1,2]. It is possible to store independently several memories, which corresponds to imprinting the trace of various spin arrangements at well separated length scales that are selected by temperature [3,4]. Similar aging, rejuvenation and memory phenomena can be observed in various other glassy systems [1], making the spin glasses conceptually simple examples for the study of out-of-equilibrium dynamics in disordered systems.

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Ageing, Rejuvenation and Memory: The Example of Spin-Glasses

Extensive experimental and numerical studies of the non-equilibrium dynamics of spin glasses subjected to temperature or bond perturbations have been performed to investigate chaos and memory effects in selected spin glass systems. Temperature shift and cycling experiments were performed on the strongly anisotropic Ising-like system {\ising} and the weakly anisotropic Heisenberg-like system {\AgMn}, while bond shift and cycling simulations were carried out on a 4 dimensional Ising Edwards-Anderson spin glass. These spin glass systems display qualitatively the same characteristic features and the observed memory phenomena are found to be consistent with predictions from the ghost domain scenario of the droplet scaling model.

Nonequilibrium dynamics of spin glasses: Examination of the ghost domain scenario

The zero-field ac susceptibility \ensuremath{\chi}(\ensuremath{\omega})=\ensuremath{\chi}'(\ensuremath{\omega})+i\ensuremath{\chi}''(\ensuremath{\omega}) of the short-range Ising spin glass ${\mathrm{Fe}}_{0.5}$${\mathrm{Mn}}_{0.5}$${\mathrm{TiO}}_{3}$ has been investigated in the vicinity of the spin-glass temperature ${\mathit{T}}_{\mathit{g}}$ in the frequency interval 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3\char21{}}$5\ifmmode\times\else\texttimes\fi{}${10}^{1}$ Hz. Because of the influence of aging, \ensuremath{\chi}(\ensuremath{\omega}) is time dependent. After a temperature quench to a temperature T\ensuremath{\le}${\mathit{T}}_{\mathit{g}}$, \ensuremath{\chi}''(\ensuremath{\omega}) is found to decrease with time. The decay towards equilibrium is logarithmic in time and the corrections to the equilibrium values of \ensuremath{\chi}''(\ensuremath{\omega}) decrease slowly with increasing frequency. At temperatures Tg${\mathit{T}}_{\mathit{g}}$ in the vicinity of the freezing temperature of \ensuremath{\chi}(\ensuremath{\omega}), a weak increase of \ensuremath{\chi}''(\ensuremath{\omega}) with time is found. By use of linear response relations, the observed time dependence of \ensuremath{\chi}''(\ensuremath{\omega}) is shown to be consistent with results from time-dependent magnetization measurements. Furthermore, the existence of an overlap length scale in spin glasses has been verified by \ensuremath{\chi}''(\ensuremath{\omega}) and time-dependent magnetization experiments.

H. Aruga Katori

Papers

Nonequilibrium dynamics of spin glasses: Examination of the ghost domain scenario

Time-dependent ac susceptibility in spin glasses.

The reentrant Ising Spin Glass Fe0.62Mn0.38TiO3 Studied with the Mössbauer Technique

Equilibrium and nonequilibrium magnetic behaviour of a reentrant Ising spin glass