Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit

Details Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit

1995-07-18

arxiv.org/abs/hep-lat/9507018v1

J.Statist.Phys. 89 (1997) 947-961

Physics

High Energy Physics

High Energy Physics - Lattice

14 pages, latex, no figures

Scientific paper

We discuss some aspects of the continuum limit of some lattice models, in particular the $2D$ $O(N)$ models. The continuum limit is taken either in an infinite volume or in a box whose size is a fixed fraction of the infinite volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be $O(1)$ and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the so-called super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called 'perfect actions'. It also shows that David's recent claim that super-instanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.

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