Dresden 2009 – wissenschaftliches Programm
DY 12.20: Poster
Dienstag, 24. März 2009, 14:30–16:30, P1A
The entropy of the Hard-Core Model mimiking disordered systems — •Andrea Winkler1, Gerold Alsmeyer1, and Andreas Heuer2 — 1Institut für mathematische Statistik WWU, 48149 Münster — 2Institut für physikalische Chemie WWU, 48149 Münster
A very simple model of particle interaction is the Hard-Core Model. Here one considers n particles on a two-dimensional square-cell lattice with N sites subject to the condition that the particles can not overlap. It can be regarded as a discrete version of the hard disc system. We calculate the entropy of this model, firstly, with the analytical method according to  and, secondly, with numerical methods via Monte-Carlo-simulations. We find a scaling relation S(ρ)=a(ρ)+b(ρ)lnc(ρ)N/N for large N and the density ρ=n/N. Futhermore the deviations for small system sizes are discussed.
 R.B.McQuistan, J.L.Hock, Composite nearest-neighbor degeneracies for several kinds of simple particles distributed on two-dimensional, square-cell lattices (J.Math.Phys 33, August 1992)