Weak randomness in geometrically frustrated systems: spin-glasses

We study the competition between the spin-glass (SG) phase and antiferromagnetic (AF), superantiferromagnetic or ferromagnetic (FE) order in geometrically frustrated systems. We consider a model with two types of frustration: one coming from disordered interactions (J) and another coming from the square-lattice Ising spin system with first-(J(1)) and second-(J(2)) neighbor interactions (intrinsic frustration). The disordered interactions are between clusters and they follow the van Hemmen model, which represents a limit of weak frustration. The cluster mean-field approximation is used to treat the short-range intercluster interactions. Results are exhibited in phase diagrams of the temperature T versus J for several values of J(2)/J(1). When the intrinsic frustration increases, the Neel and Curie temperatures decrease at the same time so that the SG phase appears at a lower J. Moreover, the FE correlations enhance the SG behavior, while AF correlations reduce the SG region at the same level of intrinsic frustration. These results indicate that a weak disorder in geometrically frustrated systems is able to stabilize the SG phase.