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

Sergio Caracciolo·Andrea Pelissetto
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Abstract

We have considered the corrections to the finite-size-scaling functions for a general class of $O(N)$ $σ$-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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Sergio Caracciolo, Andrea Pelissetto. 1996-07-04. Corrections to finite-size scaling in two-dimensional O(N) sigma-models. https://doi.org/10.1016/s0920-5632(96)00756-6

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