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Cluster self-assembly condition for arbitrary interaction potentials | Alejandro Mendoza-Coto
; Rómulo Cenci
; Guido Pupillo
; Rogelio Díaz-Méndez
; Egor Babaev
; | Date: |
9 Oct 2020 | Abstract: | We present a sufficient criterion for the emergence of cluster phases in an
ensemble of interacting classical particles with repulsive two-body
interactions. Through a zero-temperature analysis in the low density region we
determine the relevant characteristics of the interaction potential that make
the energy of a two-particle cluster-crystal become smaller than that of a
simple triangular lattice in two dimensions. The method leads to a mathematical
condition for the emergence of cluster crystals in terms of the sum of Fourier
components of a regularized interaction potential, which can be in principle
applied to any arbitrary shape of interactions. We apply the formalism to
several examples of bounded and unbounded potentials with and without
cluster-forming ability. In all cases, the emergence of self-assembled cluster
crystals is well captured by the presented analytic criterion and verified with
known results from molecular dynamics simulations at vanishingly temperatures.
Our work generalises known results for bounded potentials to repulsive
potentials of arbitrary shape. | Source: | arXiv, 2010.04631 | Services: | Forum | Review | PDF | Favorites |
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