  Given an one-dimensional Lorenz-like expanding map we prove that the
condition\linebreak $P_{top}(\phi,\partial
\mathcal{P},\ell)<P_{top}(\phi,\ell)$ (see, subsection 2.4 for definition),
introduced by Buzzi and Sarig in [1] is satisfied for all continuous potentials
$\phi:[0,1]\longrightarrow \mathbb{R}$. We apply this to prove that
quasi-H\"older-continuous potentials (see, subsection 2.2 for definition) have
at most one equilibrium measure and we construct a family of continuous but not
H\"older and neither weak H\"older continuous potentials for which we observe
phase transitions. Indeed, this class includes all H\"older and weak-H\"older
continuous potentials and form an open and [2].
