Triangular Ising antiferromagnets with quenched nonmagnetic impurities

In a random spin system, the cooperation of randomness and frustration will lead to a spin-glass phase. However, in geometrically frustrated spin systems, quenched nonmagnetic impurities lift frustration locally. This makes randomness and frustration in these systems as competitors rather than cooperators. By mapping the dilute triangular Ising antiferromagnetic system to elastic array of noncrossing strings, we find that the nonmagnetic impurities in the spin system play roles of pinning centers in the string system. Calculation shows that in the ground state of this system, the spin-glass correlation is power-law decayed, quite different from the standard behavior of spin glass in which spin-glass correlation between two spins at infinite distance tends to a finite value. This indicates that triangular Ising antiferromagnets with quenched nonmagnetic impurities cannot be a spin glass. Instead, in the ground states, they present properties of vortex glass.