Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation

Jan, 2009
33 pages
Published in:
  • J.Phys.A 42 (2009) 195401
e-Print:
Report number:
  • DAMTP-2008-116

Citations per year

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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