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arXiv:cond-mat/0102317 · The European Physical Journal B

The ± J spin glass in Migdal-Kadanoff approximation

Barbara Drossel, M A Moore

Published Jun 1, 2001• 14 citations
arXivHTMLPDF
DOI
10.1007/s100510170169

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We have studied the random-axis magnet with infinite anisotropy by three methods: Cayley-tree approximation, Migdal-Kadanoff renormalization group (MKRG), and Imry-Ma scaling. In the Cayley-tree approximation, by an examination of susceptibilities, it is shown that there exists a competition between the coordination number z and the number of components n of the spins which leads to either ferromagnetic or spin-glass order. Using the MKRG at very low temperature we map out approximately the regimes of the ferromagnetic, spin-glass, and disordered phases as a function of n and the spatial dimension, d. The Imry-Ma arguments are made as an additional method for obtaining information on the critical dimension. Comparisons of these results with the previous literature are made.
We study the non-equilibrium behaviour of three-dimensional spin glasses in the Migdal-Kadanoff approximation. This approximation is exact for disordered hierarchical lattices which have a unique ground state and equilibrium properties correctly described by the droplet model. Extensive numerical simulations show that this model lacks ageing in the remanent magnetization as well as a maximum in the magnetic viscosity in disagreement with experiments as well as with numerical studies of the Edwards-Anderson model. This result strongly limits the validity of the droplet model (at least in its simplest form) as a good model for real spin glasses.