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

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

1996-01-19

arxiv.org/abs/hep-lat/9601014v1

Phys.Rev. D54 (1996) 1736-1747

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1103/PhysRevD.54.1736

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.

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