  The regular (Bardeen)-AdS (BAdS) black hole (BH) in the extended phase space
is taken as an example for investigating the BH phase transition grade from
both macroscopic and microscopic points of view. The equation of state and
thermodynamic quantities of this BH are obtained. It is found that the BAdS BH
phase space in the extended phase space should be a second-order phase
transition near the critical point by verifying the Ehrenfest's equation, and
the possibility of its first-order phase transition can be ruled out by the
entropy continuity and the heat capacity mutation. The critical exponents from
the microscopic structure are analytically and numerically presented with the
Landau continuous phase transition theory by introducing a microscopic
order-parameter.
