Failure of crystallization for generalized Lennard–Jones potentials and coarse graining to a rotating stars problem in one dimension. (June 2023) - Crismale, V.; Kubin, A.; Ninno, A.; Ponsiglione, M.
Abstract: This paper deals with ground states for systems governed by generalized Lennard–Jones potentials L J p, q ( r ) ≔ r − p − r − q, for 0 < q < 1 < p . The energy per particle diverges to − ∞ as the number N of particles diverges. As a consequence, the average distance between particles vanishes as N → + ∞ . After suitable scaling, we prove that such a model converges, as N → + ∞ and in the sense of Γ -convergence, to a rotating stars model; the effective energy is given by the sum of a repulsive pressure term and an attractive nonlocal interaction functional. The ground states of such a limit energy have non constant density. As a consequence, for the generalized Lennard–Jones potentials considered here, crystallization does not occur in any reasonable sense.