Investigation of Size Effects on the Physical Properties of One-Dimensional Ising Models In Nano systems

Ising models in nanosystems are studied in the presence of a magnetic field. For a one-dimensional (1-D) array of spins interacting via nearest-neighbour and next-nearest-neighbour interactions we calculate the heat capacity, the surface energy, the finite-size free energy and the bulk free energy per site. The heat capacity versus temperature exhibits a common wide peak for systems of any size. A small peak also appears at lower temperatures for small arrays when the ratio of magnetic field spin interaction energy over the nearest-neighbour spin–spin interaction energy, f, is within 05 and 10. The peak becomes smaller for longer array and eventually vanishes for long arrays, disappearing when the number of spins, N, is greater than 25 when only nearestneighbour interactions are taken into account, and more than 14 when next-nearest-neighbour interactions are included as well. Ising models in which the nearest-neighbour interactions are ferromagnetic, while the next-nearest- neighbour interactions are either ferromagnetic or antiferromagnetic, are compared, and it is found that the reduced free energy in the former case exhibits a larger deviation from the bulk value.