In this brief report we explore the energy landscapes of two spin glass models using a greedy single-spin flipping process, { \tt Gmax}. The ground-state energy density of the random maximum two-satisfiability problem is efficiently approached by { \tt Gmax}. The achieved energy density $e(t)$ decreases with the evolution time $t$ as $e(t)-e(\infty)=h (\log_{ 10} t)^{ -z}$ with a small prefactor $h$ and a scaling coefficient $z > 1$, indicating an energy landscape with deep and rugged funnel-shape regions. For the $\pm J$ Viana-Bray spin glass model, however, the greedy single-spin dynamics quickly gets trapped to a local minimal region of the energy landscape.
Categories: cond-mat.dis-nn