  We investigate phase transitions and critical behaviors of the Kerr-Sen black
hole in four dimensions. Computing the involved thermodynamical quantities
including the specific heat and using the Ehrenfest scheme, we show that such a
black hole undergoes a second-order phase transition. Adopting a new metric
form derived from the Gibss free energy scaled by a conformal factor associated
with extremal solutions, we calculate the geothermodynamical scalar curvature
recovering similar phase transitions. Then, we obtain the scaling laws and the
critical exponents, matching perfectly with mean field theory.
