Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 62: Critical Phenomena and Phase Transitions

DY 62.5: Talk

Friday, March 20, 2020, 10:30–10:45, ZEU 118

Lindemann melting criterion in two dimensions — •Sergey Khrapak — Institut fuer Materialphysik im Weltraum, Deutsches Zentrum fuer Luft- und Raumfahrt (DLR), 82234 Wessling, Germany

It is well known that the conventional Lindemann's melting criterion is not applicable to two-dimensional (2D) solids, because long-wavelength density fluctuations cause the mean square displacement to diverge logarithmically with system size. Here it is demonstrated that the Lindemann's criterion can be re-formulated for 2D solids using statistical mechanics arguments. With this formulation the expressions for the melting temperature are essentially equivalent in three and two dimensions. Moreover, in two dimensions the Lindemann's melting criterion practically coincides with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young melting condition of dislocation unbinding. Examples of application are provided.