Rugged Energy Landscape
Spin glass — many local minima, simulated annealing, basin hopping
Rugged Energy Landscapes (Spin Glasses): Disordered systems like spin glasses have exponentially many local minima in their energy landscape. Finding the global minimum is NP-hard. Simulated annealing (Kirkpatrick 1983) uses high temperature T to escape local traps, then slowly cools following a schedule T→αT. Basin hopping (Wales & Doye 1997) makes large random jumps followed by local minimization — used in protein folding. The energy history shows trapping and escape events. As T→0, the system freezes in a metastable state — the spin glass phase.