Ee. Vogel et al., BOND PERCOLATION IN + -J ISING SQUARE LATTICES DILUTED BY FRUSTRATION/, Physical review. B, Condensed matter, 58(13), 1998, pp. 8475-8480
+/-J Ising lattices are exactly solved, finding all ground states. Eac
h original lattice leads to a correlated diluted lattice when all bond
s that frustrate in any of the ground states are removed. Correlation
appears in the problem when it is found that diluted lattices generate
d in this way present regions of unfrustrated bonds complemented by re
gions of frustrated (removed) bonds. The spectral distribution of size
s for unfrustrated regions is not trivial, presenting strong modulatio
ns. Here, we characterize such distribution for lattices between 16 an
d 64 spins, comparing with the monotonic distribution obtained for ran
domly generated diluted lattices. We deal with results for at least 50
0 samples in each size. About 2/3 of the samples percolate independent
ly of lattice size; percolation threshold was estimated at 0.41 for th
ese correlated diluted lattices. Most of the samples possess a large u
nfrustrated region containing about 40% of the bonds, where all spins
remain fixed in any of two states with opposite spin orientations. Suc
h a robust way of breaking ergodicity leads to high values in the site
order parameters, which implies partial or local spin-glass behavior.