Configurational degeneracy of a set of dipoles in a quasi-two-dimensional system

Abstract

The purpose of this paper is to provide an exact evaluation of the configurational degeneracy when an arbitrary number (k) of dipoles are placed in a quasi-two-dimensional space (Q2D). This Q2D is made up of three contiguous diagonals 3× N. Our Q2D space gives to the central sites of the lattice their full coordination number of nearest neighboring compartments. We are going to determine the exact configurational degeneracy W(k, N) when an arbitrary number k of the above mentioned particles are placed in this 3 × N Q2D space. We found that W(k, N) is exactly described by W(k, N) = 8W(k − 1, N − 1) − 8W(k − 2, N − 2) + W(k, N − 1) W(k, N) is a prerequisite to develop analytical methods to study the interaction between an arbitrary set of dipoles (or spins, magnetic domains, heterogeneous diatomic molecules, etc) placed in a Q2D space.