Spin-glass dynamics and the barrier model: Extraction of the Parisi physical order parameter

Abstract

Abstract The fact that the model of barrier heights monotonically increases with increasing metastable state Hamming distance (the difference between the spin orientations of any two states) on a hierarchical (ultrametric) tree can account for the ageing phenomenon in spin glasses. We make use of this model to extract spin-glass dynamics, including the instantaneous value of the zero-field-cooled magnetization M ZFC, and the time dependences of the thermoremanent magnetization M TRM(t w, t) or, equivalently, of the zero-field magnetization M ZFC(t w, t), where t is the measurement time after waiting a time t w, below the spin-glass transition temperature T g. The pure states introduced by Parisi are thought to originate from metastable states because finite barriers diverge as the temperature is lowered. These infinite barriers encompass metastable states separated by a self-similar distribution of barrier heights, independent of temperature. The model for extraction of spin-glass dynamics which we have u...