Resistivity of spin glasses below the ordering temperature

Abstract

A mean field theory of spin glasses formulated by Edwards and Anderson /1/ for classical spin systems, predicts the onset of local spin alignment leading to the formation of a condensed spin state, in which the magnetic moments of the impurity ions a r e randomly oriented with respect t o one another but locally, on any one magnetic impurity, its spin directions a r e time-correlated. The present note accounts for the reduction in the spin resistivity, a s the temperature goes below the spin glass transition temperature To, a s an effect of such local spin correlations /1, 2/, Standard procedures valid for long-range magnetization phenomena a r e modified for application to the spin glass state in the absence of external magnetic fields and found to yield a favourable comparison with experiment.Spin glasses a r e characterized by the order parameter q, which vanishes above To, and increases monotonically with decreasing temperatures below T 0' -$2')]]= 0 represents a non-vanishing correlation between the spin orientations at the same impurity at two separated instants of time. This means that at any one spin i , the thermal average <gi> = 0 below T but for the spin system a s a whole, the configuration average [[a >j] = 0 in a pure spin glass /3/, since there a r e no spin-spin correlations: <$!" -3. > = 0 at all temperatures. While the spin orientations a r e gradually "frozen in" below the transition temperature T the