We report on new high resolution SPH simulations with radiative transfer
for growing, gravitationally unstable disks (both in isolated and binary
systems). We find that fragmentation
is possible but requires a mass higher (> 0.12 Mo) than previously
estimated with simpler treatment of the radiation physics.
Convective/turbulent transport of the heat from the midplane to the
atmosphere seem to dominate the cooling of the disk  midplane rather than
radiative transport, although the result is very sensitive to the
treatment of the disk atmosphere. Higher molecular weights favour
fragmentation and are expected locally in overdense regions as spiral
shocks concentrate and vaporize ice grains.
We also show the results of the fist adaptive mesh refinement simulations
(AMR) of disks and compare them with SPH. Contrary to previous claims,
we find that both types of codes can lead to (physical) fragmentation in
similar ways once the same initial conditions are adopted. Current
criteria used to distinguish between physical and artificial fragmentation
are insufficient and only direct convergence tests can provide a reliable
answer for any type of code. This has implications for a variety of
astrophysical systems involving self-gravitating disks.