We establish the existence of freezing phase transitions in the settings of multi-dimensional shift spaces. Precisely, given an arbitrary proper subshift $X$ of a d-dimensional shift space we explicitly construct a continuous potential $\phi$ such that for all $\beta$ above some critical value $\beta_c$ the equilibrium states of $\beta\phi$ are the measures of maximal entropy of $X$, whereas for $\beta$ below $\beta_c$ no equilibrium state of $\beta\phi$ is supported on $X$. This phenomenon is referred to as a freezing phase transition for potential $\phi$ with the motivation stemming from quasicrystal models in statistical physics. To contrast this result we establish sufficient conditions on the potential which guaranty that the system never freezes. This is a joint work with J.-R. Chazottes and A. Quas.