  We compute the canonical partition for quantum black holes in the approach of
Loop Quantum Gravity (LQG). We argue that any quantum theory of gravity in
which the horizon area is built of non-interacting constituents cannot yield
qualitative corrections to the Bekenstein-Hawking (B-H) area law, but
corrections to the area law can arise as a consequence additional constraints
inducing interactions between the constituents. In LQG this is implemented by
requiring spherical horizons. The canonical approach for LQG favours a
logarithmic correction to the B-H law with a coefficient of -1/2, independently
of the area spectrum. Our initial calculation of the partition function uses
certain approximations that, we show, do not qualitatively affect the
expression for the black hole entropy. We later discuss the quantitative
corrections to these results when the simplifying approximations are relaxed
and the full LQG spectrum is dealt with. We show how these corrections can be
recovered to all orders in perturbation theory. However, the convergence
properties of the perturbative series remains unknown.
