Time and length scales in spin glasses

Abstract

Abstract. We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in the first large-scale simulation of the nonequilibrium dynamics of the three dimensional Heisenberg spin glass. Why do we study spin glass dynamics?Spin glasses can be seen as one of the paradigms for the statistical mechanics of impure materials. Experimentally, however, the spin glass phase is always probed via nonequilibrium dynamic experiments, because the equilibration time of macroscopic samples is infinite. Simulations can probe equilibrium behaviour for very moderate sizes only, so that the thermodynamic nature of the spin glass phase is still a matter of debate. It is also as a model system that the glassy dynamics of spin glasses has been studied very extensively in experiments, simulations, and theoretically in the last two decades [1,2]. Although many theories account for the simplest experimental results, such as the aging phenomenon, early experiments revealed several other spectacular phenomena (rejuvenation, memory, etc.) that are harder to explain, allowing one to discriminate between various approaches [3].In recent years, several theoretical descriptions of the slow dynamics of spin glasses described the physics in terms of a distribution of length scales whose time, t, and temperature, T , evolution depends on the specific experimental protocol, as reviewed in Ref. [3]. Aging is described as the slow growth of a coherence length, ℓ T (t), reflecting quasi-equilibrium/nonequilibrium at shorter/larger length scales. Sensitivity to perturbations of quasi-equilibrated length scales accounts then for rejuvenation effects, while the strong temperature dependence of the growth law ℓ T (t) explains memory effects [4,5,6,7,8]. If early numerical studies revealed the existence of such a distribution of length scales [9], its physical relevance was critically discussed only relatively recently [10,11]. A major problem, however, is that most studies focused on the Edwards-Anderson model of an Ising spin glass, defined by the Hamiltonian

Temperature cycles in the Heisenberg spin glass

“…in the Ising model 1 . Hence it appears potentially easier to detect chaotic temperature effects in Heisenberg systems than in Ising systems 44 , so this possibility needs to be investigated.…”

“…Numerical studies of temperature shifts and cycles in the Ising version of the model have been reported 26,27,28,29,30,31,32,33 , and temperature cycles have been discussed theoretically 34,35,36,37,38,39,40,41,42 . However, the Heisenberg spin glass model has been much less studied than its Ising counterpart, even though it is closer to many of the experimentally studied spin glass systems, and only a few aging studies exist 1,32,43,44 . In particular, extensive studies of temperature cycles have not been reported (see Ref.…”

Dislocation Glasses: Aging during Relaxation and Coarsening

“…A physical argument for the glass analogy is that the long-range interaction between dislocations can change sign as a function of relative angles, thus making frustration possible. Frustrated interactions are known to give rise to spin glasses in the presence of quenched disorder [16]. Furthermore, there is an external element of randomness in dislocation systems that arises from initial conditions.…”