We study the relaxation of interacting single--molecule magnets (SMMs) in
both spatially ordered and disordered systems. The tunneling window is assumed
to be, as in Fe8, much narrower than the dipolar field spread. We show that
relaxation in disordered systems differs qualitatively from relaxation in fully
occupied cubic and Fe_8 lattices. We also study how line shapes that develop in
''hole--digging'' experiments evolve with time t in these fully occupied
lattices. We show (1) that the dipolar field h scales as t^p in these hole line
shapes and show (2) how p varies with lattice structure. Line shapes are not,
in general, Lorentzian. More specifically, in the lower portion of the hole,
they behave as (h/t^p)^{(1/p)-1} if h is outside the tunnel window. This is in
agreement with experiment and with our own Monte Carlo results.Comment: 21 LaTeX pages, 6 eps figures. Submitted to PRB on 15 June 2005.
Accepted on 13 August 200