Phase diagram of Ising nano-particles with cubic structures

The method of variational cumulant expansion (VCE) on the Ising model is applied to investigate phase transitions in magnetic alloy nano-particles, in which a random site distribution of component atoms is assumed. By introducing the effect exchange constant, it is shown numerically that nano-particles can be treated the same way as bulk materials. The Curie temperature and the Néel temperature of binary magnetic nano-particles with cubic lattices are calculated. It is found that both the Curie temperature and the Néel temperature decrease with decreasing size of the nano-particle. Phase diagrams of binary alloy nano-particles are investigated for variable doping concentration and the results are discussed. As the nano-particle size grows larger, the critical point approaches that of a bulk. On the other hand, the tri-critical point is independent of the nano-particle size and is always the same as that of the bulk.