Equivalent Fixed-Points in the Effective Average Action Formalism

Starting from a modified version of Polchinski's equation, Morris' fixed-point equation for the effective average action is derived. Since an expression for the line of equivalent fixed-points associated with every critical fixed-point is known in the former case, this link allows us to find, for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3: published in J. Phys. A - minor change

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

Equations related to the Polchinski version of the exact renormalisation group equations for scalar fields which extend the local potential approximation to first order in a derivative expansion, and which maintain reparameterisation invariance, are postulated. Reparameterisation invariance ensures that the equations determine the anomalous dimension eta unambiguously and the equations are such that the result is exact to O(epsilon^2) in an epsilon-expansion for any multi-critical fixed point. It is also straightforward to determine eta numerically. When the dimension d=3 numerical results for a wide range of critical exponents are obtained in theories with O(N) symmetry, for various N and for a ranges of eta, are obtained within the local potential approximation. The associated eta, which follow from the derivative approximation described here, are found for various N. The large N limit of the equations is also analysed. A corresponding discussion is also given in a perturbative RG framework and scaling dimensions for derivative operators are calculated to first order in epsilon.Comment: 30 pages, 4 figures, version 2 some arguments expanded, additional reference