Corrections to finite-size scaling in two-dimensional O(N) sigma-models

Details Corrections to finite-size scaling in two-dimensional O(N) sigma-models Corrections to finite-size scaling in two-dimensional O(N) sigma-models

1996-07-04

arxiv.org/abs/hep-lat/9607013v1

Nucl.Phys.Proc.Suppl. 53 (1997) 693-695

Physics

High Energy Physics

High Energy Physics - Lattice

Talk presented at LATTICE96(other models) Postscript file avalaible at http://www1.le.infn.it:8080/~caraccio/TCMS.html

Scientific paper

10.1016/S0920-5632(96)00756-6

We have considered the corrections to the finite-size-scaling functions for a general class of $O(N)$ $\sigma$-models with two-spin interactions in two dimensions for $N=\infty$. We have computed the leading corrections finding that they generically behave as $(f(z) \log L + g(z))/L^2$ where $z = m(L) L$ and $m(L)$ is a mass scale; $f(z)$ vanishes for Symanzik improved actions for which the inverse propagator behaves as $q^2 + O(q^6)$ for small $q$, but not for on-shell improved ones. We also discuss a model with four-spin interactions which shows a much more complicated behaviour.

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