  In this work we consider black hole solutions to Einstein theory coupled to a
nonlinear power-law electromagnetic field with a fixed exponent value. We study
the extended phase space thermodynamics in canonical and grand canonical
ensembles where the varying cosmological constant plays the role of an
effective thermodynamic pressure. We examine thermodynamical phase transitions
in such black hols and find that both first and second order phase transitions
can occur in the canonical ensemble, while for the grand canonical ensemble the
Hawking-Page and second order phase transitions are allowed.
