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We mention that the Hamiltonian (1.6) with M = 2 and N ≥ 2 is physically interesting because it describes the critical properties in some structural and antiferromagnetic phase transitions, see, e.g., Refs. 49 and 2. For recent studies, see, e.g., Refs. 4, 44, 45, and references therein.
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and references therein
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This derivation assumes that the replica symmetry is not broken in the limit N → 0. This issue is discussed, e.g., in V. S. Dotsenko, J. Phys. A 32, 2949 (1999); V. V. Prudnikov, P. V. Prudnikov, and A. A. Fedorenko, Phys. Rev. B 63, 184201 (2001), and references therein.
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ν = -0.023{20} (the second error is related to the uncertainty on the coordinates of the fixed point) in agreement with the one given in the text.
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33646612191
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We are indebted with Christian Tanguy for informing us of the systematic relation of the coefficients of the series for the cubic model that corresponds to Eq. (A2).
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