Sherrington-Kirkpatrick model

The Sherrington-Kirkpatrick model (SK model) is the foundational mean-field theory of spin glasses, introduced by David Sherrington and Scott Kirkpatrick in 1975. It replaces the finite-range interactions of real magnetic materials with an idealization in which every spin interacts with every other spin through random couplings drawn from a Gaussian distribution. This infinite-range approximation makes the model mathematically tractable while preserving the essential feature of spin glasses: a rugged energy landscape with exponentially many metastable states.\n\nThe SK model was solved exactly by Giorgio Parisi in 1979 using the technique of Replica symmetry breaking, revealing that the spin glass phase is organized as an infinite hierarchy of pure states with ultrametric overlap structure. This solution showed that the low-temperature phase of a disordered system could be far more intricate than the simple ordered phases of conventional magnets. The SK model remains the theoretical reference point for understanding how systems with quenched disorder escape simple thermal equilibrium and freeze into complex, history-dependent configurations.\n\n\n