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A classical model for the lattice distortions of ${\mathrm{La}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{A}}_{\mathit{x}}$${\mathrm{MnO}}_{3}$ is derived and, in a mean field approximation, solved. The model is based on previous work by Kanamori and involves localized Mn d electrons (which induce tetragonal distortions of the oxygen octahedra surrounding the Mn) and localized holes (which induce breathing …