Rapidly converging asymptotic expansions in ± J Ising lattices

Ground-state properties of Ising lattices with different concentrations of ±J interactions are studied analytically. Rapidly converging expansions are obtained for the average frustration segment, energy per bond, and fraction of the lattice without frustration. Triangular, square and honeycomb lattices are considered. Physical properties are calculated by means of two independent theoretical methods. Numerical simulations are also carried out for sets of samples in each topology. The agreement between analytic expressions and numerical simulations is quite good in the method of the star. Such agreement improves for the method of the sublattice. Both methods are also in very good agreement with previous extensive calculations performed for the particular case of equal concentration of ±J interactions.