Fig. 8.

In-plane correlations educed by reverse Monte Carlo refinement. Correlation functions calculated from simulated vortex ensembles (open symbols) that reproduce the neutron scattering data in Fig. 7. For clarity curves are offset with a multiplication factor Y. (a) Displacement correlator $b\left(r\right)=⟨{\left({\mathbf{u}}_j-{\mathbf{u}}_l\right)}^2⟩$. (b) Hexatic orientational order $g_6\left(r\right)=⟨{\mathrm{e}}^{\mathrm{i}6\left({\theta }_j-{\theta }_l\right)}⟩$ is fitted with a single algebraic decay $\propto r^{-{\eta }_6}$. (c) Translational order $c_{\mathrm{g}}\left(r\right)=⟨{\mathrm{e}}^{\mathrm{i}\mathbf{g}.\left({\mathbf{u}}_j-{\mathbf{u}}_l\right)}⟩$ and b(r) comprise three regimes in the Bragg glass picture: the Larkin, random manifold and Bragg glass regimes (see text). Here the Larkin regime lies at indiscernibly small length scales and two-part functions fit b(r) and c_g(r) (solid lines) for the three datasets at 1.6 K. For the 0.17 T, 2.7 K dataset, which lies close to the order-disorder line, a single function fits c_g(r) corresponding to the random manifold regime