Fifth-order perturbation analysis for removing the degeneracy between squares and rhombuses

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Abstract
At the third order of the order parameter expansion, the system under study is variational, and for some range of parameters, a two-mode structure may occur. Both a square pattern and a 48° rhombic pattern are shown to minimize the free energy, while the numerical simulations of the full equations display only the squares. The expansion at the nontrivial fifth order removes the degeneracy between the two different patterns and predicts squares.