Black hole entropy in the O(N) model.

We consider corrections to the entropy of a black hole from an O(N) invariant linear σ-model. We obtain the entropy from a 1/N expansion of the partition function on a cone. The entropy arises from diagrams which are analogous to those introduced by Susskind and Uglum to explain black hole entropy in string theory. The interpretation of the σ-model entropy depends on scale. At short distances, it has a state counting interpretation, as the entropy of entanglement of the N fields φ a. In the infrared, the effective theory has a single composite field σ ∼ φ a φ a , and the state counting interpretation of the entropy is lost.