Entropy and black hole horizons

The standard approach of counting the number of eigenmodes of N scalar fields near the horizon is used as a basis to provide a simple statistical mechanical derivation of the black hole entropy in two and four dimensions. The Bekenstein formula S={A\ov 4G\h} and the two-dimensional entropy S=2M/\l\h are naturally obtained (up to a numerical constant of order 1). This approach provides an explanation on why the black hole entropy is of order 1/\h and why it is independent of the number of field-theoretical degrees of freedom.