Aging of spherical spin glasses. (English) Zbl 0993.60055
This paper studies spin glass dynamics by using an equation derived from Sherrington-Kirkpatrick’s model which normally conduces to ageing processes. The model here is considerably simpler in the sense that it is spherical and thus has a sphere as its state space. The article mainly analyzes the convergence of the solutions of a stochastic differential system as the order of the system increases and proves the so-called large deviation principle with good rate functions. As pointed out by the authors themselves, the main advantage of such simple model is that it allows to obtain rigorous proofs and a first mathematical understanding of the ageing phenomenon.
Reviewer: Guy Jumarie (Montréal)
MSC:
60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
82B44 | Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics |
60F10 | Large deviations |
82C44 | Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics |
82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
82C22 | Interacting particle systems in time-dependent statistical mechanics |
15A18 | Eigenvalues, singular values, and eigenvectors |
15B52 | Random matrices (algebraic aspects) |