Séminaire du LPTMS: Martial Mazars (LPT U-PSUD)


11:00 - 12:00

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Topological defects and the melting in two dimensions

Martial Mazars (LPT U-PSUD)

Topological defects have a preponderant role in the physics of (quasi) two-dimensional systems. One of the first applications is the description of the XY model by Kosterlitz and Thouless in the 1970s; this theoretical description of the XY model made possible in the 1980s to formulate a theory for the fusion in two dimensions, the KTHNY theory (Kosterlitz – Thouless – Halperin – Nelson – Young). In KTHNY, the transition from the solid phase to the liquid phase occurs with an intermediate phase, the hexatic phase, and each of the transitions: solid / hexatic and hexatic / liquid is of the KT type.
The microscopic mechanisms in KTHNY leading to phase transitions are dissociations of clusters of topological defects: the dissociation of dislocation pairs into free dislocations (solid / hexatic) and the dissociation of dislocations into free disclinations (hexatic / liquid). This description of the two-dimensional fusion is in competition with a first-order transition between solid and liquid, without hexatic phase.
The existence of an intermediate hexatic phase for simple systems in two dimensions remained hypothetical until the mid-2000s when it was observed in experiments on superparamagnetic colloids confined to a water-air interface (Keim, Maret 2007). This observation reinforces the relevance of KTHNY. Then, with computer simulations of hard disks (Krauth – 2011) and in colloidal systems (Thorneywork, Dullens – 2017), the hexatic / liquid transition is found to be first order, in contradiction with KTHNY.
In this seminar, we show that the mechanisms of dissociation of the KTHNY topological clusters are responsible for the solid / hexatic and hexatic / liquid transitions, and that, by a statistical analysis of the topological clusters, the KTHNY theory is compatible with a first order transition for the hexatic / liquid.

References :
– P. Keim, G. Maret and H.H. von Grünberg, 2007, Phys. Rev. E., 75, 031402.
– E.P. Bernard, W. Krauth, 2011, Phys. Rev. Lett., 107, 155704.
– A. L. Thorneywork, J. L. Abbott, D. G. A. L. Aarts and R. P. A. Dullens, 2017, Phys. Rev. Lett., 118, 158001.

The results presented in this seminar have been published in :
– M. Mazars, 2015, EPL, 110, 26003.
– M. Mazars and R. Salazar, 2019, EPL, 126, 56002.

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