Frustration in Archimedean ± J lattices

We report results on physical and topological magnitudes related to the ground level of Ising model for spins sitting at the sites of Archimedean lattice (3, 4, 6, 4), following the notation of Grünbaum and Shephard, coordination number is 4 through the lattice. We consider lattices of size N, where N represents the total number of spins, subject to periodic boundary conditions. On these systems we randomly distribute ±J nearest neighbor interactions (+J: antiferromagnetic (AF), -J: ferromagnetic (F)). Concentration x of F interactions is varied in the interval [0.0, 1.0]. We use two different methods to obtain results reported here. First, an exact numerical method related to multiple replicas, each one solved exactly for all ground states. Second, an analytical method based on probabilistic analysis of flat and curved (frustrated) plaquettes. Both methods are complementary to each other. This study aims to calculate distribution of frustrated plaquettes, energy and fractional content of unfrustrated bonds. These results are compared to similar ones reported for other Archimedean lattices, such as: square (SL), triangular (TL), honeycomb (HL), and Kagomé (KL). Conditions for a possible spin-glass (SG) phase are discussed.