Optimization of the derivative expansion in the nonperturbative renormalization group

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 67, Issue 6, 2003, Pages

  Canet, Léonie ^a   Delamotte, Bertrand ^a   Mouhanna, Dominique ^a   Vidal, Julien ^b  

^a LPTHE   (France)

^b Groupe de Physique des Solides   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CONDUCTANCE; ENERGY; INFRARED RADIATION; MATHEMATICAL MODEL; STATISTICAL ANALYSIS; THEORY;

EID: 0038746694     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.67.065004     Document Type: Article

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59. Note that the behavior of (Formula presented) given in Eq. (4) is not the most general one. For instance, (Formula presented) can be a power law cutoff, i.e., (Formula presented) in which case the constraint becomes (Formula presented) (for (Formula presented)
60. Let us notice that although the magnetization vanishes at the critical temperature, the dimensionless minimum of the fixed point potential (Formula presented) does not vanish in general.
61. (Formula presented) is defined in our calculation as minus the inverse of the relevant eigenvalue of the stability matrix, linearized around the fixed point. This computation differs from the one implemented in 54. It generates a small discrepancy (0.5%) between the (d) value in Table I and (Formula presented) computed here, see the lower curves in Fig. 44.
62. Note that several PMS solutions can lead to almost degenerate critical exponents. See for instance the curve (Formula presented) in Fig. 44 for (Formula presented) where two PMS exist at (Formula presented) and (Formula presented) In this case, either point can be selected arbitrarily, since anyway the discrepancy between (Formula presented) and (Formula presented) is negligible (it does not exceed a few tenths of percent here).
63. Actually, for (Formula presented) both (Formula presented) and (Formula presented) approach an asymptotic value for (Formula presented) that, by extending the notion of PMS to infinite (Formula presented) could be considered as a second PMS solution. However, the values of both (Formula presented) and (Formula presented) thus obtained, (Formula presented) and (Formula presented) are far from those at the second PMS of (Formula presented)–(Formula presented) and (Formula presented) and therefore cannot be considered as consistent.