We study an atomistic pair potential-energy E(n)(y) that describes the elastic behavior of two-dimensional crystals with natoms where $y\in {ℝ}^{2\times n}$ characterizes the particle positions. The main focus is the asymptotic analysis of the ground state energy asn tends to infinity. We show in a suitable scaling regime where the energy is essentially quadratic that the energy minimum of E(n) admits an asymptotic expansion involving fractional powers of n: ${\min }_y{E}^{\left(n\right)}\left(y\right)=n{E}_{\mathrm{bulk}}+\sqrt{n}{E}_{\mathrm{surface}}+o\left(\sqrt{n}\right),n\to \infty .$ The bulk energy densityEbulk is given by an explicit expression...

We study an atomistic pair potential-energy E(n)(y) that describes the elastic behavior of two-dimensional crystals with n atoms where $y\in {ℝ}^{2\times n}$ characterizes the particle positions. The main focus is the asymptotic analysis of the ground state energy as n tends to infinity. We show in a suitable scaling regime where the energy is essentially quadratic that the energy minimum of E(n) admits an asymptotic expansion involving fractional powers of n: ${\min }_y{E}^{\left(n\right)}\left(y\right)=n{E}_{\mathrm{bulk}}+\sqrt{n}{E}_{\mathrm{surface}}+o\left(\sqrt{n}\right),n\to \infty .$ The bulk energy density Ebulk is given by an explicit expression...