Properties of the ±J Ising spin glass on the triangular lattice

Abstract

We study the ground state of the ±J Ising spin glass on the triangular lattice with an arbitrary concentration p of negative bonds. In agreement with a previous study on the square lattice, it is found that the spin correlation exponent η remains constant over a range of defect concentration pc1 < p < pc2. Furthermore, the value of η obtained is 0.33 ± 0.02 which agrees, within error bars, with the square lattice result. This indicates that the spin glass phases on the two lattices are in the same universality class. However, the model on the triangular lattice has an upper critical concentration at p = pc2 that is not present for the square lattice. This transition is found to be due to a percolation of frustrated plaquettes which drives a crossover to a frustrated antiferromagnetic phase. We show that this occurs at pc2 = 0.8472 ± 0.0001 with the usual percolation exponents for two dimensions.