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

Abstract

In a finite-connectivity spin glass at the zero-temperature limit, long-range correlationsexist among the unfrozen vertices (whose spin values are non-fixed). Such long-rangefrustrations are partially removed through the first-step replica-symmetry-broken(1RSB) cavity theory, but residual long-range frustrations may still persist inthis mean-field solution. By way of population dynamics, here we performa perturbation–percolation analysis to calculate the magnitude of long-rangefrustrations in the 1RSB solution of a given spin-glass system. We study twowell-studied model systems, the minimal vertex-cover problem and the maximal2-satisfiability problem. This work points to a possible way of improving the zero-temperature1RSB mean-field theory of spin glasses.