Two Approaches to the Theory of Spin-Glasses: A Comparison with each other and with Experiment

Abstract

We use the selfconsistent Mean-Random-Field (MRF) approximation to derive the properties of spin-glasses in the random molecular field approximation. For the Gaussian distributed exchange potentials discussed by Sherrington and Kirkpatrick (SK) we obtain identical magnetic properties and a somewhat similar specific-heat to that obtained by SK who used the n → 0 expansion of the free energy derived by Edwards and Anderson. For the RKKY-potential treated in the Ising model, the MRF-method gives the very low temperature specific heat and magnetic susceptibility in excellent agreement with experiment. It similarly gives a spin-glass transition, where the transition temperature T_c∝ c^α, where c is the impurity concentration and α ≈ 0.66 for the Ising model and preliminary results give that α ≈ 0.61 for the Heisenberg model. Similarly we find that there are small but important concentration dependent correction to the “concentration independent” low temperature specific heat. A possible reason for the agreement of the Ising like model and the disagreement of the Heisenberg like prediction with experiment is given.

Part of this work supported by USAFOR Grant #73-2430B