Real-space renormalization group calculations for spin glasses and dilute magnets

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Abstract
The Edwards and Anderson model for spin glasses is investigated by a decimation rescaling transformation applied to a spin-1/2 Ising model. The technique reproduces the exactly known results for a linear chain and, in particular, predicts ordering to a spin-glass type ground state at T=0. For a two-dimensional square lattice it is shown that approximations which give qualitatively correct results in other situations predict no spin-glass transition at any temperature. A comparison is made with results for spin glasses on a Bethe lattice and with an infinite-range spin-glass model, which has been found to exhibit a transition. It is argued that the difference between infinite-range and short-range models is that the former has entirely extended eigenvectors of the random Jij matrix whereas the latter has at least some localized eigenvectors.

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