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Classical isotropic two body potentials generating martensitic transformations

An isotropic interaction potential for classical particles is devised in such a way that the crystalline ground state of the system changes discontinuously when some parameter of the potential is varied. Using this potential we model martensitic transformations, and are able to study in detail the processes that are usually associated with it: shape memory effect, superelasticity, as well as many details concerning the dynamics of the transformation, particularly the characteristics of the martensitic texture obtained as a function of parameters affecting the transformation rate. Here we introduce the interaction potentials and present some basic results about the transformation it describes, for the particular case of two dimensional triangular-rombohedral and triangular-square transformation.