We investigate the XY spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to L0ex0ex=0ex0ex12 (2D) and L0ex0ex=0ex0ex8 (3D) strongly suggest that the lower critical dimension for spin-glass ordering may be dc≈3, rather than 4 as is commonly believed. Our 3D data favor the scenario of a low but finite spin-glass ordering temperature below the chiral transition, but they are also compatible with the system being at or slightly below its lower critical dimension.
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Maucourt et al. (1998) studied this question.
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