Correlated cluster mean-field theory for spin-glass systems

The competition between cluster spin glass (CSG) and ferromagnetism or antiferromagnetism is studied in this work. The model considers clusters of spins with short-range ferromagnetic or antiferromagnetic (FE-AF) interactions (J(0)) and long-range disordered couplings (J) between clusters. The problem is treated by adapting the correlated cluster mean-field theory of D. Yamamoto [Phys. Rev. B 79, 144427 (2009)]. Phase diagrams T/J x J(0)/J are obtained for different cluster sizes n(s). The results show that the CSG phase is found below the freezing temperature T-f for lower intensities of J(0)/J. The increase of short-range FE interaction can favor the CSG phase, while the AF one reduces the CSG region by decreasing the T-f. However, there are always critical values of J(0) where AF or FE orders become stable. The results also indicate a strong influence of the cluster size in the competition of magnetic phases. For AF cluster, the increase of ns diminishes T-f reducing the CSG phase region, which indicates that the cluster surface spins can play an important role in the CSG arising.