Spin glass

Summary

A spin glass is a magnetic system whose interactions are random in sign and strength. No arrangement of the spins satisfies all of these interactions at once. In a mathematical model, the couplings between spins are random variables fixed once and for all. Each sample of the couplings gives its own Gibbs measure. Spin glasses show frustration, many competing low-energy states and a slow dynamics. Their theory, built on the replica trick and the Parisi formula, has spread to optimization, coding and neural networks.