  In this paper, we take into account the black hole solutions of Einstein
gravity with logarithmic and exponential forms of nonlinear electrodynamics. We
consider $\Lambda$ as a dynamical pressure to study the analogy of the black
holes with the Van der Waals system. We plot P-v, T-v and G-T diagrams and
investigate the phase transition of adS black holes in the canonical ensemble.
We study the nonlinearity effects of electrodynamics and see how the power of
nonlinearity affects critical behavior. We also investigate the effects of
dimensionality on the critical values and analyze its crucial role. Moreover,
we show the changes in the universal ratio P_{c}v_{c}/T_{c} for variation of
different parameters. In addition, we make a comparison between linear and
nonlinear electrodynamics and show that the lowest critical temperature belongs
to Maxwell theory. Also, we make some arguments regarding to how power of
nonlinearity brings the system to Schwarzschild-like and
Reissner-Nordstrom-like limitations. Next, we study the critical behavior in
context of heat capacity. We show that critical behavior of system is similar
to one in phase diagrams of extended phase space. We point out that phase
transition points of the extended phase space only appear as divergencies of
heat capacity. We also extend the study of phase transitions through GTD
method. We introduce two new metrics and show that divergencies of TRS of the
new metrics coincide with phase transitions. The characteristic behavior of
these divergencies, hence critical points is exactly the one that is obtained
in extended phase space and heat capacity. We also introduce a new method for
obtaining critical pressure and horizon radius by considering denominator of
the heat capacity. We show that there are several benefits that make this
approach favorable comparing to other ones.
