Random cellular structures generated from a 2D Ising ferromagnet
Renaud Delannay, G. Le Caër, Mahfuza Khatun · Journal of Physics A Mathematical and General · 1992
Topological models of 2D cellular structures are associated with distributions of spins given by a ferromagnetic Ising model with nearest-neighbour interactions on a square lattice. Every vertex of a square lattice is topologically unstable as it belongs to more than three polygons. There are two ways, associated with the spin states, to remove this degeneracy by replacing every vertex by one side. Topological properties such as the distribution P(n) of the number n of cell sides, the two-cell correlation M k (n)=P(k)A kn which is the average number of k-sided neighbours of a cell with n sides (n-cell), the mean number m(n) of sides of the first neighbour cells of n-cells are characterized as a function of T/T c , by direct calculations and by Monte Carlo and Q2R simulations. The correlations A kn of a biological tissue are compared with the A kn of a ferromagnetic Ising cellular structure and with the A kn expected from the maximum-entropy model.