Lower Critical Dimension of the XY Spin Glass

The nearest-neighbour XY spin glass on a hypercubic lattice in four dimensions is studied by Monte Carlo simulations. A finite-size scaling analysis of the data leads to a finite-temperature spin glass transition at . The critical exponents are estimated to be and . The results imply that the lower critical dimensionality for the XY spin glass is less than four.

Journal of Physics A Mathematical and GeneralAug 7, 19966 citations

Critical Properties of a Simple Spin Glass Model

Amnon Aharony A, Y. Imry

Springer eBooksJan 1, 19770 citations

Lower Critical Dimension of the XY Spin Glass

之康尾関, Yukiyasu Ozeki

Published Jan 1, 1992• 0 citations

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Springer eBooksJan 1, 19770 citations

We investigate the

\mathrm{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\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}12

(2D) and

L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8

(3D) strongly suggest that the lower critical dimension for spin-glass ordering may be ${d}_{\mathrm{c}}\ensuremath{\approx}3$, 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.