Melting of the two-dimensional solid phase in the Gaussian core model
Year: 2024
Authors: Mendoza-Coto A., Cenci R., Mattiello V., Defenu N., Nicolao L.
Autors Affiliation: Univ Fed Santa Catarina, Dept Fis, BR-88040900 Florianopolis, SC, Brazil; Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, D-01187 Dresden, Germany; Eidgeoss TH Zurich, Inst Theoret Phys, CH-8093 Zurich, Switzerland.
Abstract: A general theory for the melting of two-dimensional (2D) solids that explains the universal and nonuniversal properties remains an open problem. Although the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young theory was able to predict the critical properties of the melting transition in a variety of cases, it is already known that it could not capture the occurrence of first -order transitions observed in certain systems, nor does it provide a clear way to calculate the melting temperature for a specific model. In the present work, we have developed an analytical method that combines the self -consistent variational approximation with the renormalization group in order to deal simultaneously with the phonon fluctuations and the topological defects that are present in the melting process of 2D crystals. The method was applied with impressive success to a study of the phase diagram of the Gaussian core model, capturing not only the reentrant feature of its 2D solid phase, but also the related critical temperatures as a function of the density in quantitative detail. The developed method can be directly applied to study the melting of any hexagonal simple crystal formed by particles interacting through any finite pairwise interaction potential. Additionally, it has the potential to explain the occurrence of first -order transitions in the melting process of 2D crystals.
Journal/Review: PHYSICAL REVIEW B
Volume: 109 (6) Pages from: 64101-1 to: 64101-13
More Information: A.M.-C. acknowledges financial support from Fundacao de Amparo a Pesquisa de Santa Catarina, Brazil (Fapesc). A.M.-C. acknowledges hospitality and financial support from MPIPKS. N.D. acknowledges useful discussions with G. Giachetti. This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster).KeyWords: Long-range Order; Monte-carlo; 2 Dimensions; Molecular-dynamics; Elastic-constantsDOI: 10.1103/PhysRevB.109.064101Citations: 1data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-17References taken from IsiWeb of Knowledge: (subscribers only)