  We articulate the fact that the loop quantum gravity description of the
quantum macrostates of black hole horizons, modeled as Quantum Isolated
Horizons (QIHs), is completely characterized in terms of two independent
integer-valued `quantum hairs', viz,. the coupling constant $(k)$ of the
quantum $SU(2)$ Chern-Simons theory describing QIH dynamics, and the number of
punctures $(N)$ produced by the bulk spin network edges piercing the isolated
horizon (which act as pointlike sources for the Chern- Simons fields). We
demonstrate that the microcanonical entropy of macroscopic (both parameters
assuming very large values) QIHs can be obtained directly from the microstates
of this Chern-Simons theory, using standard statistical mechanical methods,
without having to additionally postulate the horizon as an ideal gas of
punctures, or incorporate any additional classical or semi-classical input from
general relativity vis-a-vis the functional dependence of the IH mass on its
area, or indeed, without having to restrict to any special class of spins.
Requiring the validity of the Bekenstein-Hawking area law relates these two
parameters (as an equilibrium `equation of state') and consequently allows the
Barbero-Immirzi parameter to take any real and positive value depending on the
value of $k/N$. The logarithmic correction to the area law obtained a decade
ago by R. Kaul and one of us (P.M.), ensues straightforwardly, with precisely
the coefficient -3/2, making it a signature of the loop quantum gravity
approach to black hole entropy.
