  We report significant alteration of the equilibrium properties of the
superconductor HgBa$_2$Ca$_2$Cu$_3$O$_x$ when correlated disorder in the form
of randomly oriented columnar tracks is introduced via induced fission of
Hg-nuclei. From studies of the equilibrium magnetization $M_{eq}$ and the
persistent current density over a wide range of temperatures, applied magnetic
fields, and track densities up to a ``matching field'' of 3.4 Tesla, we observe
that the addition of more columnar tracks acting as pinning centers is
progressively offset by reductions in the magnitude of $M_{eq}$. Invoking
anisotropy induced ``refocusing'' of the random track array and incorporating
vortex-defect interactions, we find that this corresponds to increases in the
London penetration depth $\lambda$; this reduces the vortex line energy and
consequently reduces the pinning effectiveness of the tracks.
