Configurational Degeneracy of a Set of Dipoles in a Quasi-two-dimensional System.

P. L. DAMMIG QUIÑA; V. E. PASTOR; I. M. IRURZUN; E. E. MOLA

JOURNAL OF MATHEMATICAL CHEMISTRY

SPRINGER

Año: 2010 p. 592 - 600

0259-9791

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 coor-dination 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 dia-tomic molecules, etc) placed in a Q2D space.