We present a computer simulation study of the phase behavior of two-dimensional classical particles repelling each other through an isotropic core-softened potential. As in the analogous three dimensional case, a reentrant-melting transition occurs upon compression for not too high pressures. However, in two dimensions in the low density part of the phase diagram melting is a continuous two-stage transition, with an intermediate hexatic phase. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario for this melting transition. On the other hand, at high density part of the phase diagram one first-order transition takes place. We expect that such a phenomenology can be checked in confined monolayers of charge-stabilized colloids with a softened core and water confined between two hydrophobic plates.
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