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A renormalization-group approach could be formulated with a Landau-Ginzburg effective free energy as a function of the order-parameter field (Formula presented). The fact that in a particular ordered configuration, only one of the ordering wave vectors can be present, translates to a "cubic" anisotropy in order-parameter space favoring the three coordinate axes. This implies a first-order phase transition [see D. J. Wallace, J. Phys. C 6, 1390 (1973)].
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Wallace, D.1
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J. F. Fernandez, H. A. Farach, C. P. Poole and M. Puma, Phys. Rev. B 27, 4274 (1983).
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and compare also W. G. Wilson, Phys. Lett. A 137, 398 (1989)].
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4243390367
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This situation is similar to the problem of propagating order in, e.g., the three-state Potts antiferromagnet on a triangular lattice, where a single chain of bonds is insufficient to force the relationship between two clusters [see J. Adler, R. G. Palmer and H. Meyer, Phys. Rev. Lett. 58, 882 (1987).
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25744444598
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this is not true for a frustrated system such as the fcc antiferromagnet (compare Ref. 30) owing to its frustration and this complicates the propagation of order
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and H. Fried and M. Schick, Phys. Rev. B 41, 4389 (1990)]. However, that problem is unfrustrated, in that the restriction of a pure system ground state to the sites of the diluted system is always one of the valid ground states; this is not true for a frustrated system such as the fcc antiferromagnet (compare Ref. 30) owing to its frustration and this complicates the propagation of order.
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Fried, H.1
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S. Shapira, L. Klein, J. Adler, A. Aharony and A. B. Harris, Phys. Rev. B 49, 8830 (1994).
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On the basis of simulations, it is argued by R. Kühn and A. Huber, Phys. Rev. Lett. 73, 2268 (1994) and by J.-K. Kim and A. Patrascioiu, ibid. 72, 2785 (1994), that the critical exponents of unfrustrated diluted Ising models show a nonuniversal dilution dependence.
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Huber, A.1
Patrascioiu, A.2
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0000397729
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Recently, N. Kawashima and A. P. Young [Phys. Rev. B 53, 484 (1996)] have found evidence for a finite transition temperature and ordering below (Formula presented) for the ±J Ising spin glass, indicating that the lower critical dimension is indeed below 3. Their critical exponents (ν=1.7±0.3 and η=-0.35±0.05), are slightly different from those found earlier (ν≈1.2 and η ≈-0.25). A comparison with the exponents of the present simulation suggests that the diluted fcc AFM and the Ising ±J spin glass do not lie in the same universality class.
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Phys. Rev. B
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