A dynamical treatment of the spin glass transition
- 20 November 1984
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 17 (32), 5759-5784
- https://doi.org/10.1088/0022-3719/17/32/011
Abstract
Closed non-linear equations are derived through mode-coupling approximations for the correlation functions and susceptibilities for the Edwards-Anderson model of a classical Heisenberg system with nearest-neighbour random exchange couplings. These equations, which exhibit full dynamical stability, lead to a self-consistent treatment of spin-density propagation and spin-current relaxation. They are found to describe a transition from a paramagnetic to a spin glass phase, which is viewed as one where the dynamics changes from ergodic to a non-ergodic behaviour. Near the critical temperature Tc the low-frequency correlation functions are obtained as dynamical scaling laws governed by a critical frequency omega c, which slows down proportionally to epsilon 2, with epsilon =(T-Tc)/Tc. Approaching the critical point from the paramagnetic side the diffusivity vanishes linearly with epsilon . The susceptibility exhibits a symmetric cusp. The drastic changes of the spin dynamics at the transition point show up most clearly for the spin-current spectra. The numerical solution of the equations is discussed.Keywords
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