Bond percolation in Ising square lattices diluted by frustration

(Formula presented) Ising lattices are exactly solved, finding all ground states. Each original lattice leads to a correlated diluted lattice when all bonds that frustrate in any of the ground states are removed. Correlation appears in the problem when it is found that diluted lattices generated in this way present regions of unfrustrated bonds complemented by regions of frustrated (removed) bonds. The spectral distribution of sizes for unfrustrated regions is not trivial, presenting strong modulations. Here, we characterize such distribution for lattices between 16 and 64 spins, comparing with the monotonic distribution obtained for randomly generated diluted lattices. We deal with results for at least 500 samples in each size. About (Formula presented) of the samples percolate independently of lattice size; percolation threshold was estimated at 0.41 for these correlated diluted lattices. Most of the samples possess a large unfrustrated region containing about 40% of the bonds, where all spins remain fixed in any of two states with opposite spin orientations. Such a robust way of breaking ergodicity leads to high values in the site order parameters, which implies partial or local spin-glass behavior.