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We study an atomistic pair potential-energy E(n)(y) that describes the elastic behavior of two-dimensional crystals with natoms where 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: 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
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:
The bulk energy density Ebulk is given by an explicit
expression...
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