  Inspired by Conti and Zanzotto \cite{Conti2004A}, we reformulate a simple
variational model for reconstructive phase transitions in crystals arising in
continuum mechanics in the framework of Landau's theory of phase
transition(with slight modification). We provide and prove that this class of
modular invariant functions admit exactly hexagonal-square lattices minimizers
without passing through rhombic lattices, being the first rigorous result in
this regard. Our result gives an affirmative answer to an open problem by in
\cite{Conti2004A}. In addition, our result has independent interest from number
theory.
