In this paper, we review several important features of the out-of-equilibrium dynamics of spin glasses. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low temperature phase. We report in particular new results on the sub-aging behaviour of spin glasses. We then discuss the rejuvenation...

We survey the recent mathematical results about aging in certain simple disordered models. We start by the Bouchaud trap model. We then survey the results obtained for simple models of spin-glass dynamics, like the REM (the Random Energy Model, which is well approximated by the Bouchaud model on the complete graph), then the spherical Sherrington-Kirkpatrick model. We will insist on the differe...

Abstract. We consider quantum-dynamical phenomena in the SU(2), S = 1/2 infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical selfconsistency equations. Using the Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic states we study in particular the isotropic model variant on the spin space. Two complemen...

In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are Gaussian, on the scale 1/ √ N , for N large. The method we employ is based on the idea, we recently developed, of introducing quadratic coupling between two r...

(Reçu le 14 octobre 1980, revise le 16 decembre, accepte le 22 decembre 1980) Résumé. 2014 Dans cette lettre, nous calculons la moyenne gelée (sans répliques) pour des verres de spin avec désordre local. Ceci permet une définition naturelle du champ moyen. On montre que les champs moyens décrivant les verres de spin sont du type instanton. Abstract. 2014 In this letter we perform quenched avera...

When a spin glass is cooled down, a memory of the cooling process is imprinted in the spin structure. This memory can be disclosed in a continuous heating measurement of the ac-susceptibility. E.g., if a continuous cooling process is intermittently halted during a certain aging time at one or two intermediate temperatures, the trace of the previous stop(s) is recovered when the sample is contin...

We have analyzed a fermionic infinite-ranged quantum Heisenberg spin glass with BCS coupling in real space in the presence of a magnetic field. It has been possible to locate the transition line between the normal paramagnetic phase (NP) and the phase where there is a long range order corresponding to pair formation in sites (PAIR). The nature of the transition line is also investigated. This t...

We study for random quantum spin systems the energy gap between the ground and first excited states to clarify a relation to the spin-glass–paramagnetic phase transition. We find that for the transverse Sherrington-Kirkpatrick model the vanishing of the averaged gap does not identify the transition. A power-law form of the gap distribution function leads to power-law distributions of the linear...