Classical annealing of the Sherrington-Kirkpatrick spin glass using Suzuki-Kubo mean-field Ising dynamics

We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo mean-field Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction field). The resultant dynamics, starting from any arbitrary paramagnetic phase (with local magnetizations m₈=±1, for the ith spin, and the global magnetization m=0), takes the system quickly to an appropriate state with small local values of magnetization (m₈) commensurate with the (frustrated) interactions. As the temperature decreases with the annealing, the configuration practically remains (in an effective adiabatic way) close to a low-energy configuration as the magnitudes of m₈'s and the spin glass order parameter q grow to unity. While the configuration reached by the procedure is not the ground state, for an N-spin SK model (with N up to 10 000), the deviation in the energy per spin E₍^0-E^0 found by the annealing procedure scales as N^-2/3, with E^0=-0. 7629±0. 0002, suggesting that in the thermodynamic limit the energy per spin of the low-energy configurations converges to the ground state of the SK model (analytical estimate being E^0=-0. 7631667265⋯), fluctuation σ₍ in E₍^0 decreases as ∼N^-3/4, and the annealing time τ₍∼N, making this protocol highly efficient in estimating the ground state energy of the SK model.