  The effects of power-law Maxwell field on the Van der Waals like phase
transition of higher-dimensional dilaton black holes are probed in detail. It
is shown that the Smarr relation gains corrections due to the effects of both
the power-law Maxwell field and the dilaton field while thermodynamic volume is
exactly the same as that of Einstein-Maxwell-dilaton black holes. We
successfully derive the analytic solutions of critical point and carry out some
check to ensure that these critical quantities are positive. It is shown that
the constraint on the parameters turns out to be $0<\alpha^2<1$, which is more
tighter than that in the non-extended phase space. It is also shown that these
critical quantities and the ratio $P_cv_c/T_c$ are affected by the power-law
Maxwell field. Moreover, critical exponents are found to coincide with those of
other AdS black holes, showing the powerful influence of mean field theory.

General Relativity and Quantum Cosmology