The Lower Critical Dimension of the XY Spin Glass

Details The Lower Critical Dimension of the XY Spin Glass The Lower Critical Dimension of the XY Spin Glass

1997-09-17

arxiv.org/abs/cond-mat/9709197v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 ps figures. Typos have been corrected, one reference has been added and the concluding paragraph has been expanded.

Scientific paper

10.1103/PhysRevLett.80.770

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.

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