LONG-TIME MAGNETIZATION RELAXATION OF SPINS DIFFUSING IN A RANDOM FIELD

We study the free-induction decay and the spin-echo attenuation at long times for spins diffusing in a random magnetic field. We show that the decay of transverse magnetization in a Gaussian random longitudinal field is asymptotically M(t) approximately t(y-1) e(-t/tau), where gamma is the exponent of a self-avoiding walk. The usual result given by a cumulant expansion fails due to correlations arising from multiple self-intersections in d less-than-or-equal-to 4. Experimental relevance of our analysis is discussed along with the question of universality and the existence of large fluctuations in finite-size systems.