Dynamic scaling and the field-dependent critical line in a fractal cluster model of spin glasses

We extend an earlier fractal cluster model of spin glasses to study (1) the magnetization relaxation M(t) induced by a magnetic field, (2) magnetic noise, and (3) dynamics near a critical line Tg(H). Above the zero-field transition temperature Tg, M(t) follows a stretched exponential form exp(-t^1-n) with n={ν}z/({φ}+{ν}z), where {φ},{ν}, and z are standard static and dynamical critical exponents. A dynamic scaling relation is derived for the entire region Tg(H)Tg in agreement with experiments. The equations associated with lines of constant relaxation time are obtained and it is shown how nonuniversality of exponents along the critical line can be tested.