Related Issues On Triangular Antiferromagnetic Ising Model

In this thesis we investigate triangular antiferromagnetic Ising model and related is-sues. In a random spin system, the cooperation of randomness and frustration will lead to aspin-glass phase. However, in geometrically frustrated spin systems, quenched nonmagnet-ic impurities lift frustration locally. This makes randomness and frustration in these systemsas competitors rather than cooperators. By mapping the dilute triangular Ising antiferromag-netic system to elastic array of noncrossing strings, we find that the nonmagnetic impuritiesin the spin system play roles of pinning centers in the string system. Calculation shows thatin the ground state of this system, the spin-glass correlation is power-law decayed, quitedi?erent from the standard behavior of spin glass in which spin-glass correlation betweentwo spins at infinite distance tends to a finite value. This indicates that triangular Isingantiferromagnets with quenched nonmagnetic impurities cannot be a spin glass. Instead,in the ground states, they present properties of vortex glass. Because of the great groundstate macroscopic degeneracy of the triangular antiferromagnetic Ising model, a small fieldperturbation will induce great instabilities. For the triangular antiferromagnetic Ising modelunder a magnetic field, the system can be mapped into an XY model with Lock-in potentialthrough the string mapping method. As the magnetic field is su?ciently small, the lock-inpotential can be treated as a perturbation. Through renormalization analysis, we can get therecursion relations between the field and the newly defined XY coupling constant. Furthermore, we can get the renormalization ?ow diagram by the recursion relations. Calcula-tion shows that at zero temperature a su?ciently small field will not induce phase transition.