Finite-size scaling characterization of the ±J diluted Ising lattice

Square lattices with (±J) exchange interactions between nearest-neighbor spins have been analyzed by using an Ising Hamiltonian. The ground-state properties are numerically evaluated by computational techniques. The energy per bond, the site correlation parameter and the fraction of unfrustrated bond are averaged over 3000 samples randomly selected. The number of spin N considered were N= 16, 25, 36, 49, 64, 81, 100, and 144. After removing all the frustrated bonds from any of the ground-state, the remaining lattice, called diluted lattice, has been characterized by means of finite-size scaling. The percolation threshold h_gc, for the diluted lattice is h_gc = 0.4, which is less than the corresponding threshold for classical random percolation, i.e. h_c = 0.5. Critical exponents like the correlation lenght and the order parameter exponents, ν and β respectively, were also obtained for the diluted lattice. The results are compared with the well-known random percolation problem. Significant qualitative differences are shown and discussed.