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This paper demonstrates that the Lindemann's criterion can be re-formulated in two dimensions using statistical mechanics arguments. The resulting explicit expression for the melting temperature appears formally equivalent to that in three dimensions. The result is practically equivalent to the the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young melting condition of dislocation unbinding.
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S. A. Khrapak (2020) studied this question.
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