Properties of Spin Glasses

• transition to a ``glassy'' phase at low temperatures

• susceptibility has a cusp rather than a divergence at

• very large number of metastable states (local minimum of energy) in spin glass phase

• long equilibration times (logarithmic rather than exponential relaxation to equilibrium) --- remanent magnetization

• degeneracy (or near-degeneracy) of ground state, with many configurations having (nearly) the lowest energy value

• finding ground states is a difficult (NP hard) problem

• main properties of real spin glasses (e.g. amorphous alloys) can be described fairly well by spin glass Ising model on a regular crystalline lattice