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(-t1-n) with n=1/2z/(+1/2z), where ,1/2, and z are standard static and dynamical critical exponents. A dynamic scaling relation is derived for the entire region Tg(H)<T<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. © 1986 The American Physical Society.