Hard Core entropy: lower bounds

We establish lower bounds for the entropy of the Hard Core Model on a few 2d lattices $\scriptstyle {\rm {\bf L}}.$ In this model the allowed configurations inside $\scriptstyle \{0,1\}^{{\rm {\bf L}}}$ are the one's in which the nearest neighbor $\scriptstyle 1$'s are forbidden. Our method which is based on a sequential fill-in scheme is unbiassed and thereby yields in principle arbitrarily good estimates for the topological entropy. The procedure also gives some detailed information on the support of the measure of maximal entropy.