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

TL;DR

This paper investigates residual long-range frustrations in zero-temperature 1RSB solutions of finite-connectivity spin glasses, using perturbation-percolation analysis to quantify frustrations and suggest improvements to mean-field theories.

Contribution

It introduces a perturbation-percolation method to measure long-range frustrations in 1RSB solutions of spin-glasses, enhancing understanding of residual correlations.

Findings

Residual long-range frustrations can be quantified in 1RSB solutions.

The method is applied to vertex-cover and 2-satisfiability problems.

Results suggest potential improvements to mean-field theories.

Abstract

In a finite-connectivity spin-glass at the zero-temperature limit, long-range correlations exist among the unfrozen vertices (whose spin values being non-fixed). Such long-range frustrations are partially removed through the first-step replica-symmetry-broken (1RSB) cavity theory, but residual long-range frustrations may still persist in this mean-field solution. By way of population dynamics, here we perform a perturbation-percolation analysis to calculate the magnitude of long-range frustrations in the 1RSB solution of a given spin-glass system. We study two well-studied model systems, the minimal vertex-cover problem and the maximal 2-satisfiability problem. This work points to a possible way of improving the zero-temperature 1RSB mean-field theory of spin-glasses.