  We investigate the thermodynamics of critical phenomena in Born-Infeld AdS
black holes using a canonical ensemble. The critical behavior has been studied
near the critical point which is characterized by a discontinuity in the heat
capacity at constant charge. We explicitly calculate the critical exponents of
the relevant thermodynamic quantities. These exponents satisfy all the
thermodynamic scaling laws. We also check the Generalized Homogeneous Function
(GHF) hypothesis (or the scaling hypothesis) which is shown to be compatible
with the thermodynamic scaling laws. Finally we check the validity of the
scaling laws of second kind which include the critical exponents associated
with the spatial correlation. In the appropriate limit our results also provide
the corresponding expressions for the Reissner Nordstrom AdS case.
