  We propose and use a novel, hybrid Monte Carlo algorithm that combines
configurational bias particle swaps with parallel tempering. We use this new
method to simulate a standard model of a glass forming binary mixture above and
below the so-called mode-coupling temperature, Tmct. We find that an ansatz
that was used previously to extrapolate thermodynamic quantities to
temperatures below Tmct breaks down in the vicinity of the mode-coupling
temperature. Thus, previous estimates of the so-called Kauzmann temperature
need to be reexamined. Also, we find that the Adam-Gibbs relations D ~
exp(-a/TSc) and tau ~ exp(b/TSc), which connect the diffusion coefficient D and
the relaxation time tau with the configurational entropy Sc, are valid for all
temperatures for which the configurational and vibrational contributions to the
free energy decouple.
