Iterating Block Spin Transformations of the O(3) Non-Linear Sigma-Model

Abstract

We study the iteration of block spin transformations in the O(3) symmetric non-linear sigma-model on a two-dimensional square lattice with help of the Monte Carlo method. In contrast to the classical Monte Carlo Renormalization Group approach, we do attempt to explicitly compute the block spin effective actions. Using two different methods for the determination of effective couplings, we study the renormalization group flow for various parametrization and truncation schemes. The largest ansatz for the effective action contains thirteen coupling constants. Actions on the renormalized trajectory should describe theories with no lattice artefacts, even at small correlation length. However, tests with the step scaling function of Luescher et al. reveal that our truncated effective actions show sizable scaling violations indicating that the ansaetze are still too small.

29 pages (latex, including 4 postscript figures, uuencoded gz-compressed .tar file 46Kb )

References in corpus (7)

• The classically perfect fixed point action for SU(3) gauge theory
• Non--perturbative tests of the fixed point action for SU(3) gauge theory
• Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model
• The absence of cut--off effects for the fixed point action in 1--loop perturbation theory
• Canonical Demon Monte Carlo Renormalization Group
• Scaling and topology in the 2-d O(3) $\sigma$-model on the lattice with the fixed point action
• The Shape of the Renormalized Trajectory in the Two-dimensional O(N) Non-linear Sigma Model

Cited by in corpus (7)

• Effective lattice theories for Polyakov loops
• The nature of the continuum limit in the 2D $R{P}^2$ gauge model
• Fixed-Point Actions in 1-Loop Perturbation Theory
• Perfect Scalars on the Lattice
• Continuous phase transition of a fully frustrated XY model in three dimensions
• Effective sigma models and lattice Ward identities
• Block Spin Effective Action for 4d SU(2) Finite Temperature Lattice Gauge Theory