Relationship between the structure of the ground level and frustration in ±J Ising lattices

Ground states of Ising lattices with ±J exchange interactions (bonds) are highly degenerate. Such degeneracy can be grouped in sets of local ensembles (LEGs) in which states are connected by single spin flips. Here we study LEGs in samples 6×6. Then we go onto the decomposition of the total ground-state degeneracy into partial degeneracies of the LEGs. Each LEG can be generated by flipping spins grouped into clusters, whose sizes are directly related to the degeneracies of the LEGs. We find that all bonds attached to a cluster are frustrated in an itinerant way. Additionally, there is rigid frustration that can be local (associated to some LEGs) or global (associated to all LEGs). The rest of the bonds constitute the diluted (unfrustrated) lattice possessing interesting properties.