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This is proved only for simplified spring models.","posed_since":"1968","precise":"For a 2D classical particle system with a smooth pair potential whose ground state is triangular, prove at low T a Gibbs state in which the bond-orientation field $\\psi_6(x)=\\sum \\text{ over neighbors of } \\exp(6 i \\theta)$ has nonzero mean, $\\theta$ the bond angle. Merkl, Rolles (2009), Heydenreich, Merkl, Rolles (2014) and Aumann (2015) prove orientational order for harmonic-spring models on a fixed triangulation, with limited or arbitrary defects; the case where particles move freely and neighbors change is open.","problem_ref":null,"references":"","settled_by":"A proof of nonzero mean bond orientation for a genuine 2D continuum Gibbs point process at low temperature.","status_note":"Spring models with fixed connectivity are settled (Aumann 2015); continuum particle systems are not.","title":"Long-range bond-orientational order in 2D particle 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