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arXiv · 1309.6278

O(N) Models with Topological Lattice Actions

Wolfgang Bietenholz·Michael Bögli·Urs Gerber·Ferenc Niedermayer·Michele Pepe·Fernando G. Rejón-Barrera·Uwe-Jens Wiese
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Abstract

A variety of lattice discretisations of continuum actions has been considered, usually requiring the correct classical continuum limit. Here we discuss "weird" lattice formulations without that property, namely lattice actions that are invariant under most continuous deformations of the field configuration, in one version even without any coupling constants. It turns out that universality is powerful enough to still provide the correct quantum continuum limit, despite the absence of a classical limit, or a perturbative expansion. We demonstrate this for a set of O(N) models (or non-linear $σ$-models). Amazingly, such "weird" lattice actions are not only in the right universality class, but some of them even have practical benefits, in particular an excellent scaling behaviour.

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Wolfgang Bietenholz, Michael Bögli, Urs Gerber, Ferenc Niedermayer, Michele Pepe, Fernando G. Rejón-Barrera, Uwe-Jens Wiese. 2013-09-24. O(N) Models with Topological Lattice Actions. https://arxiv.org/abs/1309.6278

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