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Ground state energy E0 (blue, lower data) and first excited state energy E1 (orange, upper data) for the graph (filled circles) and corresponding continuous disk (empty circles). The solid lines are the asymptotic continuum formulas from Eq. (17). Inset: Partition function Z summed over negative energies for the graph with ℓ = 4 (blue) and associated disk (red) as a function of inverse temperature f. The dashed line is the low-temperature asymptote ln Z ~ −βE0.
