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 N^5/6 (N is the number of spins). Results are confirmed by Monte Carlo simulation and numerical solution of the TAP equations.

Authors: C. Dasgupta and H. Sompolinsky
Year of publication: 1983
Journal: Phys. Rev. B 27, 4511(R) – Published 1 April 1983

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“Working memory”