Journal of Mathematical Chemistry

, Volume 48, Issue 3, pp 592–600 | Cite as

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
Original Paper


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 × NQ2D 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.


Dipoles Configurational degeneracy Entropy Partition function 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • P. L. Dammig Quiña
    • 1
  • V. E. Pastor
    • 1
  • I. M. Irurzun
    • 1
  • E. E. Mola
    • 1
    • 2
  1. 1.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, INIFTA. Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET. Facultad de Ciencias ExactasUniversidad Nacional de La PlataLa PlataRepública Argentina
  2. 2.Facultad de Química e Ingeniería, Fray Roger BaconRosario Pontificia Universidad Católica ArgentinaBuenos AiresArgentina

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