and $S({\bf K}_2)$ is small, or vice versa, giving a large value of $|\Delta S|$; above melting, the system is in a liquid state with the same symmetry as the underlying grid, so $S({\bf K}_1)=S({\bf K}_2)$ by reflection symmetry and $\Delta S=0$.

Anticipating a first order vortex lattice melting transition, we slowly cool down a $20\times 20 \times 6$ size system from high temperature using ordinary Metropolis Monte Carlo until we reach a temperature at which we observe the system to switch back and forth between large and small values of $\Delta S$ during the course of the simulation. As an example of this, we show in Fig. \[f3\]a a plot of $\Delta S/S_0$ vs. simulation time ($S_0\equiv S(0)=fL^2$) at a temperature close to the melting transition $T_{\rm m}(p)$ for a moderate value of disorder strength $p=0.12$. In Fig. \[f3\]b we show an intensity plot of $\ln S({\bf k}_\perp)$, averaged over only those configurations in Fig. \[f3\]a which have $\Delta S/S_0 >0.1$. We see sharp Bragg peaks of high intensity at the reciprocal lattice vectors ${\bf K}_1$ indicating that this is the vortex lattice state. In Fig. \[f3\]c we show show an intensity plot of $\ln S({\bf k}_\perp)$, averaged now 