  The critical behavior of magnetically charged by rational nonlinear
electrodynamics (RNED) AdS black holes in an extended phase space is
investigated. The cosmological constant is considered as a thermodynamic
pressure and the black hole mass is identified with the chemical enthalpy. The
analogy with the Van der Waals liquid-gas system is found and the critical
exponents coincide with those of the Van der Waals system. The thermodynamics
of RNED-AdS black holes and phase transitions are studied. A new thermodynamic
quantities conjugated to the nonlinear parameter of RNED and a magnetic charge
are defined. It is demonstrated the consistency of the first law of black hole
thermodynamics and the Smarr formula.

General Physics