  We study the transport and equilibration properties of a classical Heisenberg
chain, whose couplings are random variables drawn from a one-parameter family
of power-law distributions. The absence of a scale in the couplings makes the
system deviate substantially from the usual paradigm of diffusive spin
hydrodynamics, and exhibit a regime of subdiffusive transport with an exponent
changing continuously with the parameter of the distribution. We propose a
solvable phenomenological model that correctly yields the subdiffusive
exponent, thereby linking local fluctuations in the coupling strengths to the
long-time, large-distance behaviour. It also yields the finite-time corrections
to the asymptotic scaling, which can be important in fitting the numerical
data. We show how such exponents undergo transitions as the distribution of the
coupling gets wider, marking the passage from diffusion to a regime of slow
diffusion, and finally to subdiffusion.
