## Hard Square Entropy Constant

N.B. A detailed on-line essay by S. Finch was the starting point for this entry.

Let be the number of binary Matrices with no adjacent 1s (in either columns or rows). Define , then the hard square entropy constant is defined by

The quantity arises in statistical physics (Baxter et al. 1980, Pearce and Seaton 1988), and is known as the entropy per site of hard squares. A related constant known as the Hard Hexagon Entropy Constant can also be defined.

References

Baxter, R. J.; Enting, I. G.; and Tsang, S. K. Hard-Square Lattice Gas.'' J. Statist. Phys. 22, 465-489, 1980.

Finch, S. Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/square/square.html

Pearce, P. A. and Seaton, K. A. A Classical Theory of Hard Squares.'' J. Statist. Phys. 53, 1061-1072, 1988.