## Close to close packing

### Authors: Oliver Penrose and George Stell

ABSTRACT

For various lattice gas models with nearest neighbour exclusion (and, in one case, second-nearest neighbour exclusion as well), we obtain lower bounds on $m$, the average number of particles on the non-excluded lattice sites closest to a given particle. They are all of the form $$m/m_{cp} \ge 1 - \hbox{~const.}(N_{cp}/N - 1)$$ where $N$ is the number of occupied sites, $m_{cp}$ is the coordination number, snd $N_{cp}$ is the value of $N$ at close packing. An analogous result exists for hard disks in the plane.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-35.ps.gz