Annals of Combinatorics 3 (1999) 191-203


Planar Lattice Gases with Nearest-Neighbor Exclusion

R.J. Baxter

Theoretical Physics, I.A.S. and School of Mathematical Sciences, The Australian National University, Canberra, ACT 0200, Australia
RJ.Baxter@anu.edu.au

Received November 27, 1998

AMS Subject Classification: 05B20, 82B20, 82B80

Abstract. We discuss the hard-hexagon and hard-square problems, as well as the corresponding problem on the honeycomb lattice. The case when the activity is unity is of interest to combinatorialists, being the problem of counting binary matrices with no two adjacent 1's. For this case, we use the powerful corner transfer matrix method to numerically evaluate the partition function per site, density and some near-neighbor correlations to high accuracy. In particular, for the square lattice, we obtain the partition function per site to 43 decimal places.

Keywords: combinatorics, statistical mechanics, legal matrices, lattice models, nearest-neighbor exclusion, hard squares, hard hexagons


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