Asymptotics of the IDS for Schr\"{o}dinger operators with singular potentials and Gibbs point processes

The asymptotic behavior of the integrated density of states (IDS), $N(E)$, is investigated for random Schr\"{o}dinger operators with a single-site potential $V$ satisfying $\mathrm{essinf}\, V = -\infty$. Under the assumption that the underlying point process is a Gibbs point process with repulsive pairwise interactions, the leading term of $\log N(E)$ as $E \to -\infty$ is determined using a periodic approximation method. It is shown that repulsive pairwise interactions lead to a significantly faster decay of $N(E)$ compared to the Poisson case. Furthermore, configurations with multiple clusters can provide the dominant contribution to the IDS in the Gibbs setting, contrasting with the single-cluster dominance typically observed in Poisson models. Finally, refined estimates of the leading constants are provided for specific classes of potentials, including those with multiple singularities.