  In equilibrium statistical mechanics or thermodynamics formalism one of the
main objectives is to describe the behavior of families of equilibrium measures
for a potential parametrized by the inverse temperature $\beta$. Here we
consider equilibrium measures as the shift invariant measures that maximizes
the pressure. Other constructions already prove the chaotic behavior of these
measures when the system freezes, that is, when $\beta\rightarrow+\infty$. One
of the most important examples was given by Chazottes and Hochman where they
prove the non-convergence of the equilibrium measures for a locally constant
potential when the dimension is bigger then 3. In this work we present a
construction of a bidimensional example described by a finite alphabet and a
locally constant potential in which there exists a subsequence
$(\beta_k)_{k\geq 0}$ where the non-convergence occurs for any sequence of
equilibrium measures at inverse of temperature $\beta_k$ when
$\beta_k\rightarrow+\infty$. In order to describe such an example, we use the
construction described by Aubrun and Sablik which improves the result of
Hochman used in the construction of Chazottes and Hochman.
