Abstract :
In this work, one and two-dimensional lattices are studied theoretically by a statistical mechanical approach. The nearest and next-nearest neighbor interactions are both taken into account, and the approximate thermodynamic properties of the lattices are calculated. The results of our calculations show that: (1) even thought the next-nearest nieghbor interaction may have an inisignificant effect on the entropy of either the almost purely ordered or disordered phase, it does have a significant effect on the entropy of the lattice when the order-disorder transition is taking place. (2) The next-nearest neighbor interaction broadens the range of temperature on which the transition occure. (3) The transition takes place more slowly with respect to temperature, when the next-nearest neighbor interaction is considered. (4) The average temperature, at which the transition occure, shifts to a higher one when there is an increase in the next-nearest neighbor interaction.
