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In a finite-connectivity spin-glass at the zero-temperature limit, long-rangecorrelations exist among the unfrozen vertices (whose spin values beingnon-fixed). Such long-range frustrations are partially removed through thefirst-step replica-symmetry-broken (1RSB) cavity theory, but residuallong-range frustrations may still persist in this mean-field solution. By wayof population dynamics, here we perform a perturbation-percolation analysis tocalculate the magnitude of long-range frustrations in the 1RSB solution of agiven spin-glass system. We study two well-studied model systems, the minimalvertex-cover problem and the maximal 2-satisfiability problem. This work pointsto a possible way of improving the zero-temperature 1RSB mean-field theory ofspin-glasses.

Long-range frustration in T=0 first-step replica-symmetry-broken solutions of finite-connectivity spin glasses