Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points
Jun 6, 200133 pages
Published in:
- Nucl.Phys.B 612 (2001) 340-372
e-Print:
- cond-mat/0106105 [cond-mat.stat-mech]
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Abstract: (Elsevier)
We investigate the critical behavior that d -dimensional systems with short-range forces and an n -component order parameter exhibit at Lifshitz points whose wave-vector instability occurs in an m -dimensional isotropic subspace of R d . Utilizing dimensional regularization and minimal subtraction of poles in d=4+ m 2 −ϵ dimensions, we carry out a two-loop renormalization-group (RG) analysis of the field-theory models representing the corresponding universality classes. This gives the beta function β u ( u ) to third order, and the required renormalization factors as well as the associated RG exponent functions to second order, in u . The coefficients of these series are reduced to m -dependent expressions involving single integrals, which for general (not necessarily integer) values of m ∈(0,8) can be computed numerically, and for special values of m analytically. The ϵ expansions of the critical exponents η l 2 , η l 4 , ν l 2 , ν l 4 , the wave-vector exponent β q , and the correction-to-scaling exponent are obtained to order ϵ 2 . These are used to estimate their values for d =3. The obtained series expansions are shown to encompass both isotropic limits m =0 and m = d .Note:
- 42 pages, 1 figure; to appear in Nuclear Physics B; footnote added, minor changes in v2
- 05.20.-y
- 11.10.Kk
- 64.60.Ak
- 64.60.Fr
- Field theory
- Critical behavior
- Anisotropic scale invariance
- Lifshitz point
- renormalization group
- critical phenomena
References(52)
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