  The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is
extended, taking the inverse of the GB coupling constant as a new thermodynamic
pressure $P_{\mathrm{GB}}$. We studied the critical behavior associated with
$P_{\mathrm{GB}}$ in the extended thermodynamic phase space at fixed
cosmological constant and electric charge. The result shows that when the black
holes are neutral, the associated critical points can only exist in five
dimensional GB-AdS black holes with spherical topology, and the corresponding
critical exponents are identical to those for Van der Waals system. For charged
GB-AdS black holes, it is shown that there can be only one critical point in
five dimensions (for black holes with either spherical or hyperbolic
topologies), which also requires the electric charge to be bounded within some
appropriate range; while in $d>5$ dimensions, there can be up to two different
critical points at the same electric charge, and the phase transition can occur
only at temperatures which are not in between the two critical values.
