Journal of Statistical Physics

, Volume 159, Issue 4, pp 972–986 | Cite as

Existence of Ground States of Nonlocal-Interaction Energies



We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that this condition is closely related to the notion of stability (i.e. \(H\)-stability) of pairwise interaction potentials. Our approach uses the direct method of the calculus of variations.


Ground states Global minimizers H-stability Pair potentials Self-assembly Aggregation 

Mathematics Subject Classification

49J45 82B21 82B05 35R09 45K05 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Robert Simione
    • 1
  • Dejan Slepčev
    • 1
  • Ihsan Topaloglu
    • 2
  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

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