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 though the
next-nearest neighbor interaction may have an insignificant 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 occurs. (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 occurs, shifts to a higher one when there is an
increase in the next-nearest neighbor interaction