  In one and two dimensions, transport coefficients may diverge in the
thermodynamic limit due to long--time correlation of the corresponding
currents. The effective asymptotic behaviour is addressed with reference to the
problem of heat transport in 1d crystals, modeled by chains of classical
nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium
numerical simulations confirm that the finite-size thermal conductivity
diverges with the system size $L$ as $\kappa \propto L^\alpha$. However, the
exponent $\alpha$ deviates systematically from the theoretical prediction
$\alpha=1/3$ proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev.
Lett. {\bf 89}, 200601 (2002)].
