The Lower Critical Dimension of the XY Spin Glass

Abstract

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 L=12 (2D) and L=8 (3D) strongly suggest that the lower critical dimension for spin-glass ordering may be $d_c\approx 3$ rather than four 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.

4 pages, 3 ps figures. Typos have been corrected, one reference has been added and the concluding paragraph has been expanded. To appear in Phys. Rev. Lett

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