Spin glass - Wikipedia
statistical-physicscondensed-matterdisordered-systemsneural-networks
Abstraction: Disordered magnetic system with frustrated interactions and non-ergodic phases
Key points:
- A spin glass has random mixture of ferromagnetic and antiferromagnetic bonds creating geometrical frustration; spins freeze at a "freezing temperature" T_f below which the system is non-ergodic
- The Edwards-Anderson (EA) model (1975) uses a nearest-neighbor Ising Hamiltonian with bond couplings drawn from a Gaussian distribution; defines the order parameter q = replica correlation
- The Sherrington-Kirkpatrick (SK) model (1975) extends to infinite-range interactions; Giorgio Parisi solved it in 1979 using replica symmetry breaking with infinitely many order parameters
- Below T_f the system is trapped in a hierarchically disordered energy landscape with ultrametric structure between minima; ergodicity is broken
- Parisi's replica symmetry breaking solution contributed to his 2021 Nobel Prize in Physics
- Applications beyond physics: Hopfield neural networks, optimization, protein folding funnel model; replica mean-field theory computes neural network storage capacity
Connections: Giorgio Parisi · David Sherrington · Spin Glass · Replica Method · Mean Field Theory