  We study the electron spin resonance (ESR) of low-dimensional spin systems at
high temperature, and test the Kubo-Tomita theory of exchange narrowing. In
finite-size systems (molecular magnets), we found a double-peak resonance which
strongly differs from the usual Lorentzian. For infinite systems, we have
predictions for the linewidth and lineshape as a function of the anisotropy
strength. For this, we have used an interpolation between a non-perturbative
calculation of the memory function at short times (exact diagonalization) and
the hydrodynamic spin-diffusion at long times. We show that the
Dzyaloshinskii-Moriya anisotropies generally induce a much larger linewidth
than the exchange anisotropies in two dimensions, contrary to the
one-dimensional case.
