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Prove this power law for a particle system.","posed_since":"1968","precise":"For a 2D continuum particle system with triangular ground state at low T, prove that the translational correlation $\\langle \\rho_G(x) \\rho_G(0)*\\rangle$, $G$ a reciprocal lattice vector of the triangular lattice, decays as $\\mid x\\mid^{-\\eta_G(T)}$ with $\\eta_G(T)\\to 0$ as $T\\to 0$ (quasi-long-range order), with matching upper and lower power-law bounds.","problem_ref":null,"references":"","settled_by":"Upper and lower power-law bounds on positional correlations with exponent vanishing as $T \\to 0$.","status_note":"Absence of true positional order for 2D continuum particles is proved (Richthammer 2007).","title":"Power-law decay of positional correlations in 2D 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