  In this paper we have studied the critical phenomena in higher curvature
charged black holes in the anti-de Sitter (AdS) space-time. As an example we
have considered the third order Lovelock-Born-Infeld black holes in AdS
space-time. We have analytically derived the thermodynamic quantities of the
system. Our analysis revealed the onset of a higher order phase transition in
the black hole leading to an infinite discontinuity in the specific heat at
constant charge at the critical points. Our entire analysis is based on the
canonical framework where we have fixed the charge of the black hole. In an
attempt to study the behavior of the thermodynamic quantities near the critical
points we have derived the critical exponents of the system explicitly.
Although the values of the critical points have been determined numerically,
the critical exponents are calculated analytically. Our results fit well with
the thermodynamic scaling laws. The scaling hypothesis is also seen to be
consistent with these scaling laws. We find that all types of AdS black holes,
studied so far, indeed belong to the same universality class. Moreover these
results are consistent with the mean field theory approximation. We have
derived the suggestive values of the other two critical exponents associated
with the correlation function and correlation length on the critical surface.
