Equivalence of statistical-mechanical and dynamic descriptions of the infinite-range Ising spin-glass

We prove the equivalence between the dynamic mean-field theory of the Ising spin-glass and the statistical-mechanical theory of Thouless, Anderson, and Palmer (TAP). Individual low-free-energy TAP solutions describe short-time properties, whereas thermodynamic equilibrium corresponds to averaging over all such solutions. The square of the staggered magnetization associated with the largest eigenvalue of the interaction matrix scales as N56 (N is the number of spins). Results are confirmed by Monte Carlo simulation and numerical solution of the TAP equations.