Replica trick - Wikipedia

Abstraction: Statistical physics technique averaging log partition function via integer replicas

Key points:

• Uses the identity log Z = lim_{n->0} (Z^n - 1)/n to convert disorder-averaging of log Z into averaging of Z^n (easier for integer n via Gaussian integrals)
• The mathematical contradiction of treating n as integer then taking n->0 has never been formally resolved, yet results match all known exact solutions
• Replica symmetry breaking (RSB) is sometimes needed for physical results; it is associated with ergodicity breaking and slow dynamics in disordered systems
• Applied beyond condensed matter to information theory, signal processing, error-correcting codes, and compressed sensing
• The cavity method and supersymmetric method are alternative approaches; the latter is rigorous but only for non-interacting systems
• Giorgio Parisi used RSB to solve the Sherrington-Kirkpatrick spin glass model in 1979, work that contributed to his 2021 Nobel Prize

Connections: Giorgio Parisi · Spin Glass · Replica Method · Quenched Disorder

Source: http://en.wikipedia.org/wiki/Replica_trick