Geodesic
Renormalization group study of the~melting of a~two-dimensional system of collapsing hard disks
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 424-440

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We consider the melting of a two-dimensional system of collapsing hard disks (a system with a hard-disk potential to which a repulsive step is added) for different values of the repulsive-step width. We calculate the system phase diagram by the method of the density functional in crystallization theory using equations of the Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young theory to determine the lines of stability with respect to the dissociation of dislocation pairs, which corresponds to the continuous transition from the solid to the hexatic phase. We show that the crystal phase can melt via a continuous transition at low densities (the transition to the hexatic phase) with a subsequent transition from the hexatic phase to the isotropic liquid and via a first-order transition. Using the solution of renormalization group equations with the presence of singular defects (dislocations) in the system taken into account, we consider the influence of the renormalization of the elastic moduli on the form of the phase diagram.
Keywords: melting of two-dimensional system, Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young theory, elastic modulus
Mots-clés : hexatic phase. 
@article{TMF_2017_191_3_a4,
     author = {V. N. Ryzhov and E. E. Tareeva and Yu. D. Fomin and E. N. Tsiok and E. S. Chumakov},
     title = {Renormalization group study of the~melting of a~two-dimensional system of collapsing hard disks},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {424--440},
     publisher = {mathdoc},
     volume = {191},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a4/}
}
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V. N. Ryzhov; E. E. Tareeva; Yu. D. Fomin; E. N. Tsiok; E. S. Chumakov. Renormalization group study of the~melting of a~two-dimensional system of collapsing hard disks. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 424-440. http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a4/