Plaquette distributions for ±J Ising lattices

Physical magnitudes of +/-J Ising systems are determined by their topological properties which depend on the number of frustrated plaquettes and on the distribution of curved plaquettes through the lattice. In the present paper, we consider two-dimensional lattices (3 homogeneous and 3 mixed lattices) and polyhedra (5 regular and 5 semi-regular). For small systems 3 different methods are used to find the abundance of curved plaquettes as function of x the concentration of ferromagnetic interactions. Coincidence among results is very good. In this way the function giving the probability for curved plaquettes is informed for 16 different systems. An application to obtain ground state energy in some cases is done at the end. (C) 2004 Elsevier B.V. All rights reserved.