Growing Length Scale(s) and Spin Glass Ground State(s)

Abstract:
  Spin glasses are paradigmatic examples of systems with quenched disorder. At sufficiently low temperature, Tc, they are thought to pass from a paramagnetic phase to an ordered, spin-glass phase. Despite thirty years of study, however, the nature of this possible spin-glass phase remains controversial. Experiment can provide no easy answers since at temperatures near and below Tc, spin glass dynamics slows dramatically and, consequently, all macroscopic spin glass systems are far from equilibrium. But as time passes spatial correlations must evolve in a system that begins in a random initial condition, so that the length scale, L_{eq}(t_w), over which spin glasses are locally equilibrated must grow with waiting time, t_w. In many classical systems, we understand the growth of such domains of local order. In Ising ferromagnets, for example, they correspond roughly to regions of up and down order, in which spins have correlations characteristic of infinite equilibrated systems. In spin glasses, on the other hand, development of local equilibrium is ill-understood, even qualitatively. What is the form of spin-glass order that develops? How many different long-time states can be observed in a given system region of scale-L? How do these relate to any putative infinite system equilibrium order in the first place? I will introduce a framework for posing and then addressing these questions and will provide a limited set of answers.