For Schrödinger operators with singular potentials on repulsive Gibbs point processes, log N(E) decays faster as E goes to negative infinity than in the Poisson case, with multi-cluster configurations sometimes dominating the leading term.
Georgii, Gibbs Measures and Phase Transitions(2nd ed.), de Gruyter Studies in Mathematics
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Asymptotics of the IDS for Schr\"{o}dinger operators with singular potentials and Gibbs point processes
For Schrödinger operators with singular potentials on repulsive Gibbs point processes, log N(E) decays faster as E goes to negative infinity than in the Poisson case, with multi-cluster configurations sometimes dominating the leading term.