Comment on ``Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory,'' [X. Hu, Phys. Rev. Lett. 87, 057004 (2001)]

Details Comment on ``Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory,'' [X. Hu, Phys. Rev. Lett. 87, 057004 (2001)] Comment on ``Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory,'' [X. Hu, Phys. Rev. Lett. 87, 057004 (2001)]

2002-03-26

arxiv.org/abs/cond-mat/0203533v1

Physics

Condensed Matter

Superconductivity

2 pages

Scientific paper

We show that, in the most general $N$-component theory with symmetry O(n_1)+O(n_2), N=n_1+n_2\geq 3, the O(N)-symmetric fixed point has (at least) three unstable directions: the temperature, the quadratic anisotropy, and the spin-4 quartic perturbation. This implies that in the SO(5) theory of high-$T_c$ superconductivity an additional tuning is required to obtain an enlarged SO(5) symmetry. This is in contrast with the recent numerical results reported by Hu, Phys. Rev. Lett. 87, 057004 (2001). \

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