Lower Critical Dimension of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="italic">XY</mi></math></span> Spin-Glass Model

J. Maucourt; D. R. Grempel

doi:10.1103/PhysRevLett.80.770

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Lower Critical Dimension of the $XY$ Spin-Glass Model

J. Maucourt and D. R. Grempel

Département de Recherche Fondamentale sur la Matière Condensée, SPSMS, CENG, 17, rue des Martyrs, 38054 Grenoble Cedex 9, France

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Phys. Rev. Lett. 80, 770 – Published 26 January, 1998

DOI: https://doi.org/10.1103/PhysRevLett.80.770

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 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.

References (19)

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[c1] J. Villain, J. Phys. C 10, 4793 (1977); 11, 745 (1978).

[c2] H. Kawamura and M. Tanemura, J. Phys. Soc. Jpn. 60, 608 (1991).

[c3] P. Ray and M. A. Moore, Phys. Rev B 45, 5361 (1992).

[c4] H. Kawamura, J. Phys. Soc. Jpn. 61, 3062 (1992).

[c5] H. Kawamura, Phys. Rev B 51, 12 398 (1995).

[c6] In a recent preprint (cond-mat/9703162), S. Jain has suggested that this may not be true in four dimensions.

[c7] S. Jain and A. P. Young, J. Phys. C 19, 3913 (1986).

[c8] J. R. Banavar and M. Cieplak, Phys. Rev. Lett. 48, 832 (1982); M. Cieplak and J. R. Banavar, Phys. Rev. B 29, 469 (1984).

[c9] W. L. McMillan, Phys. Rev. B 31, 342 (1985).

[c10] B. M. Morris, S. G. Colborne, M. A. Moore, A. J. Bray, and J. Canisius, J. Phys. C 19, 1157 (1986).

[c11] H. Nishimori and Y. Ozeki, J. Phys. Soc. Jpn. 59, 289 (1990).

[c12] M. Schwartz and A. P. Young, Europhys. Lett. 15, 209 (1991).

[c13] Y. Ozeki and H. Nishimori, Phys. Rev. B 46, 2879 (1992).

[c14] L. R. Walker and R. E. Walstedt, Phys. Rev. B 22, 3816 (1980).

[c15] P. Gawiec and D. R. Grempel, Phys. Rev. B 44, 2613 (1991).

[c16] P. Gawiec, D. R. Grempel, and J. Maucourt (to be published).

[c17] R. N. Bhatt and A. P. Young, Phys. Rev. Lett. 54, 245 (1985); Phys. Rev. B 37, 5606 (1988).

[c18] H. F. Cheung and W. L. McMillan, J. Phys. C 16, 7027 (1983).

[c19] F. Matsubara, T. Iyota, and S. Inawashiro, Phys. Rev. Lett. 67, 1458 (1991).

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Lower Critical Dimension of the $XY$ Spin-Glass Model

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Lower Critical Dimension of the XY Spin-Glass Model

Abstract

References (19)

Lower Critical Dimension of the $XY$ Spin-Glass Model