Numerical study of the spin-glass transition in a dilute Ising model on a triangular lattice

We study an Ising model with nearest-neighbor antiferromagnetic interactions. It is placed on a triangular lattice, where each site is occupied by a spin with x probability. There is no applied magnetic field. Randomness and frustration, two essential ingredients of spin-glasses, are present in this model. We study its critical properties here. The entropy is obtained by a transfer-matrix calculation as a function of x at low temperature (T=0.3JkB) for systems on a lattice of 10 ×{} 20 sites. A fairly shallow minimum appears near x0.9, which suggests that this case is the one most likely to show a transition into an ordered state at low temperature. We study the cases x=1, 0.9, and 0.74, which is about half-way to the critical percolation. We simulate systems on lattices of 50 ×{} 50 sites and 30 ×{} 30 sites by the Monte Carlo method. The specific heat has a broad maximum at T0.9 for x=0.74 and 0.9. χSG, defined by χSG=N^-1Σi,j^〈σᵢσⱼ〉², and the relaxation time (τ) are obtained for T≥0.6JkB. Both quantities, τ and χSG, turn out to be proportional to exp[A(T-T₀)ᶜ] and 0≤T₀0.4; a fit with T₀=0 yields c≈1 for $x=1$ but c≈2 for x=0.74 and 0.9.