  The aim of this article is to establish freezing phase transition of the
pressure function, considering the generalized Hofbauer potential {\phi}, which
is connected to the distance from subshift of finite type {\Sigma}F in the full
shift {\Sigma} over finite alphabets. Our objective is to prove that the
pressure function exhibits phase transition with the dominating measure is
highly concentrated on {\Sigma}F after the transition. Moreover, the pressure
function attains C1-smoothness when the transition occurs at 2.
