system do not appear to be decreasing (or perhaps vanishing) as the system size increases. The need to keep the transverse system length $L$ a multiple of 5, so as to remain commensurate with the vortex lattice periodicity, and the difficulty of equilibrating hops between lattice and liquid states as the system size, and hence to the total free energy barrier between theses state, increases, limits greatly the range of system sizes that we can consider. In Table \[tab1\] we show our results for the three system sizes $20\times 20\times 6$, $30\times 30\times 6$ and $20\times 20\times 12$, for the specific disorder strength $p=0.12$. We see that while $T_{\rm m}$ decreases slightly as the system size increases, $[\Delta E]$ remains remain roughly independent of size while $[\Delta Q]$ shows a slight increase. We also compute the spread in melting temperatures $\Delta T_{\rm m}$ that we find as we consider different independent realizations of the quenched random disorder $\{\epsilon_{i\mu}\}$. If the system is self averaging over the quenched disorder, we would expect that $\Delta T_{\rm m}\propto 1/\sqrt{V}$, with $V=L^2L_z$ the system volume. In Table \[tab1\] we therefore also give the value for $\Delta T_{\rm m}\sqrt{V}$ for the three system sizes. Considering 