Locality of Critical Thresholds in Spin Glasses

In spin glass systems, the critical threshold $JC$ determines whether a given bond with a strength of $J_{ij}$ is satisfied or not. It had been observed that when $J_{ij}$ crosses $JC$, the induced system ground state changes are often drastic. However, the response of other bonds' $JC$ to the $J_{ij}$ change is not as drastic: specifically, it typically decays with the distance between the target bond's $JC$ and the changed $J_{ij}$. Utilizing this characteristic, we have designed a method to assess the accuracy of locally computing the ground state in Edwards-Anderson spin glasses.