The absence of cut--off effects for the fixed point action in 1--loop perturbation theory

Abstract

In order to support the formal renormalization group arguments that the fixed point action of an asymptotically free model gives cut--off independent physical predictions in 1--loop perturbation theory, we calculate the finite volume mass--gap $m(L)$ in the non--linear $\sigma$--model. No cut--off effect of the type $g^4{\left(a/L\right)}^n$ is seen for any $n$. The results are compared with those of the standard and tree level improved Symanzik actions.

arXiv comment8 pages (latex) + 1 figure (Postscript), uuencoded

References in corpus (4)

• Perfect lattice action for asymptotically free theories
• Finite size and temperature effects in the AF Heisenberg model
• The classically perfect fixed point action for SU(3) gauge theory
• Non--perturbative tests of the fixed point action for SU(3) gauge theory

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• Corrections to Finite-Size Scaling in the Lattice N-Vector Model for Infinite N
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• Perfect Lattice Actions for Staggered Fermions
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• Fixed-Point Actions in 1-Loop Perturbation Theory
• Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
• Classical improvement of lattice actions and quantum effects: a unified view
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• Testing the efficiency of different improvement programs
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