Table of Contents
Physics Research International
Volume 2010, Article ID 284231, 5 pages
Research Article

Bicritical Central Point of 𝐽 F N − 𝐽 S N Ising Model Phase Diagram

1Laboratoire de Physique de la Matière Condensée, Faculté des Sciences Ben M'sik, Université Hassan II, Casablanca, Morocco
2Laboratoire de Physique de la Matière Condensée, Faculté des Sciences El Jadida, Université Chouaib Doukkali, Casablanca, Morocco

Received 16 September 2010; Accepted 6 November 2010

Academic Editor: Harold Zandvliet

Copyright © 2010 Yahia Boughaleb et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We deal with a 2D half occupied square lattice with repulsive interactions between first and second neighboring particles. Despite the intensive studies of the present model the central point of the phase diagram for which the ratio of the two interaction strengths 𝑅 = 𝐽 S N / 𝐽 F N = 0 . 5 is still open. In the present paper we show, using standard Monte Carlo calculations, that the situation corresponds to a phase of mixed ordered structures quantified by an “algebraic” order parameter defined as the sum of densities of the existing ordered clusters. The introduced grandeur also characterizes the transitions towards the known pure ordered phases for the other values of 𝑅 as mentioned by the agreement of our results with those of the literature. The computation of the Cowley short range order parameter against 𝑅 suggests that the central point is bicritical and is a state to cross when passing between the two pure phases.