Ap. Gottlob et al., ITERATING BLOCK SPIN TRANSFORMATIONS OF THE O(3) NONLINEAR SIGMA-MODEL, Physical review. D. Particles and fields, 54(2), 1996, pp. 1736-1747
We study the iteration of block spin transformations in the O(3) symme
tric nonlinear sigma model on a two-dimensional square lattice with th
e help of the Monte Carlo method. In contrast with the classical Monte
Carlo renormalization group approach, we do attempt to explicitly com
pute the block spin effective actions. Using two different methods for
the determination of effective couplings, we study the renormalizatio
n group flow for various parametrization and truncation schemes. The l
argest ansatz for the effective action contains thirteen coupling cons
tants. Actions on the renormalized trajectory should describe theories
with no lattice artifacts, even at a small correlation length. Howeve
r, tests with the step scaling function of Luscher, Weisz, and Wolff r
eveal that our truncated effective actions show sizable scaling violat
ions indicating that the Ansatze are still too small.