Chaos in short-range spin glasses

Abstract

The nature of static chaos in Ising spin glasses is studied. For the problem of chaos with magnetic field, scaling relations in the case of the SK model and short-range models are presented. Our results also suggest that if there is de Almeida-Thouless line then it is similar to that of mean-field theory for d=4 and close to the h=0 axis for d=3. We estimate the lower critical dimension to be in the range 2.7-2.9. Numerical studies at d=4 show that there is chaos against temperature changes dT and the correlation length diverges like 1/dT.

10 pages+3 figures on request, Latex file