  While 2D Gibbsian particle systems might exhibit orientational order
resulting in a lattice-like structure, these particle systems do not exhibit
positional order if the interaction between particles satisfies some weak
assumptions. Here we investigate to which extent particles within a box of size
$2n \times 2n$ may fluctuate from their ideal lattice position. We show that
particles near the center of the box typically show a displacement at least of
order $\sqrt{log n}$. Thus we extend recent results on the hard disk model to
particle systems with fairly arbitrary particle spins and interaction. Our
result applies to models such as rather general continuum Potts type models,
e.g. with Widom-Rowlinson or Lenard-Jones-type interaction.
