Fig. \[f2\]b we show the vortex structure function $S({\bf k}_\perp)$ for each of these two ground state orientations. We find sharp Bragg peaks at reciprocal lattice vectors ${\bf K}$. For the vortex lattice of Fig. \[f2\]a there are only four non-zero reciprocal lattice vectors, related to one another by $\pi/2$ rotations of $k$-space. For the two possible ground state orientations, we label these two disjoint sets of reciprocal lattice vectors by ${\bf K}_1$ and ${\bf K}_2$ as shown in Fig. \[f2\]b.

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At finite but small disorder strength, $p\le p_c\simeq 0.22$, we continue to find at low temperatures a vortex lattice with the same symmetry as that of Fig. \[f2\]a. The existence of the two possible orientations for this state motivates our definition of the following order parameter for the vortex lattice to liquid melting transition. If we denote by $S({\bf K}_1)$ and $S({\bf K}_2)$ the value of the vortex structure function averaged over the four non-zero reciprocal lattice vectors of each orientation respectively, then the difference, $\Delta S\equiv S({\bf K}_1)-S({\bf K}_2)$, will signal the vortex lattice melting transition: below melting, the system has ordered into one of the two possible vortex lattice orientations, and so $S({\bf K}_1)$ is large 