Spin glasses: the hole story

Abstract
A theory of the dynamics of vector spin glasses is developed based on the assumption that the system stays in the vicinity of a particular local minimum of the Hamiltonian ('hole') for macroscopic times. This implies long relaxation times for spin glasses provided that a typical 'hole' has a high density of directions for which the energy surface is locally 'flat'. This picture is exemplified by analytic results for the long-range Sherrington-Kirkpatrick model (1975), while numerical simulations support the validity of its predictions for two and three-dimensional spin glasses.

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