@article{51fe40b3083845a78902f5a32fc91c2e,

title = "Crystallization for Coulomb and Riesz interactions as a consequence of the Cohn-Kumar conjecture",

abstract = "The Cohn-Kumar conjecture states that the triangular lattice in dimension 2, the E8 lattice in dimension 8, and the Leech lattice in dimension 24 are universally minimizing in the sense that they minimize the total pair interaction energy of infinite point configurations for all completely monotone functions of the squared distance. This conjecture was recently proved by Cohn-Kumar-Miller-Radchenko-Viazovska in dimensions 8 and 24. We explain in this note how the conjecture implies the minimality of the same lattices for the Coulomb and Riesz renormalized energies as well as jellium and periodic jellium energies, hence settling the question of their minimization in dimensions 8 and 24.",

keywords = "Abrikosov lattice, Cohn-Kumar conjecture, Coulomb interaction, Crystallization, Jellium, Renormalized energy, Riesz interaction, Triangular lattice, Wigner crystal",

author = "Mircea Petrache and Sylvia Serfaty",

note = "Funding Information: The first author was supported by the Fondecyt Iniciaci?n grant number 11170264 entitled {"}Sharp asymptotics for large particle systems and topological singularities{"}. The second author was supported by NSF grant DMS-1700278 and by a Simons Investigator grant. Funding Information: Received by the editors September 6, 2019. 2010 Mathematics Subject Classification. Primary 52C35, 52C99, 82C05, 82C22, 11H06, 11H31. Key words and phrases. Crystallization, Cohn-Kumar conjecture, Coulomb interaction, Riesz interaction, jellium, renormalized energy, Abrikosov lattice, triangular lattice, Wigner crystal. The first author was supported by the Fondecyt Iniciaci{\'o}n grant number 11170264 entitled “Sharp asymptotics for large particle systems and topological singularities”. The second author was supported by NSF grant DMS-1700278 and by a Simons Investigator grant. Publisher Copyright: {\textcopyright} 2020 American Mathematical Society.",

year = "2020",

month = jul,

doi = "10.1090/proc/15003",

language = "English (US)",

volume = "148",

pages = "3047--3057",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "7",

}