Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation
Jan, 200933 pages
Published in:
- J.Phys.A 42 (2009) 195401
e-Print:
- 0901.0450 [hep-th]
Report number:
- DAMTP-2008-116
View in:
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Abstract: (arXiv)
Equations related to the Polchinski version of the exact renormalisation group equations which generalise the local potential approximation to first order in a derivative expansion, and which maintain the crucial property of reparameterisation invariance, are postulated. They allow a precise determination of the anomalous dimension eta which is exact to O(epsilon^2) in an epsilon-expansion and which is straightforward to use numerically when the dimension d=3. Numerical results for a wide range of critical exponents in theories with O(N) symmetry, for various N and for a range of eta, are obtained. The numerical results for eta when d=3 for various N are also given. The large N limit of the equations is also discussed. A corresponding discussion is also given in a perturbative RG framework and scaling dimensions for derivative operators are calculated to first order in epsilon.Note:
- 30 pages, 4 figures
- 64.60.Fr
- 64.60.Kw
- 68.35.Rh
- 11.10.Gh
- 64.60.Ak
- 11.10.-z
- Exact Renormalisation Group
- Derivative Expansion
- Reparametrisation Invariance
- expansion: derivative
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