Mainini, Edoardo; Piovano, Paolo; Stefanelli, Ulisse Finite crystallization in the square lattice. (English) Zbl 1292.82043 Nonlinearity 27, No. 4, 717-737 (2014). Summary: This paper addresses two-dimensional crystallization in the square lattice. A suitable configurational potential featuring both two- and three-body short-ranged particle interactions is considered. We prove that every ground state is a connected subset of the square lattice. Moreover, we discuss the global geometry of ground states and their optimality in terms of discrete isoperimetric inequalities on the square graph. Eventually, we study the aspect ratio of ground states and quantitatively prove the emergence of a square macroscopic Wulff shape as the number of particles grows. Cited in 31 Documents MSC: 82D25 Statistical mechanics of crystals Keywords:crystallization; square lattice; atomic interaction potentials; boundary energy; edge isoperimetric inequality PDFBibTeX XMLCite \textit{E. Mainini} et al., Nonlinearity 27, No. 4, 717--737 (2014; Zbl 1292.82043) Full Text: DOI Link