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One such potential suffices.","problem_ref":null,"references":"","settled_by":"A construction, for example by a multiscale or Pirogov-Sinai-type expansion around the crystal, of a non-translation-invariant Gibbs measure for one continuum potential in 3D.","status_note":"Proved for lattice models via Pirogov-Sinai theory, and positional order is ruled out for 2D continuum systems (Richthammer 2007); as of 2026 no continuum system in $d \\ge 3$ has a proof of a crystalline Gibbs state.","title":"Broken translation symmetry for a 3D continuum particle 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