Phase Transition in Subshifts of Finite Type via Hofbauer Potential

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