F. Farchioni — Page 4

arXiv1995

The absence of cut--off effects for the fixed point action in 1--loop perturbation theory

In order to support the formal renormalization group arguments that the fixed point action of an asymptotically free model gives cut--off independent physical predictions in 1--loop perturbation theory, we calculate the finite volume mass--gap $m(L)$ in the non--linear $σ$--model. No cut--off effect of the type $g^4\left(a/L\right)^n$ is seen for any $n$. The results are compared with those of the standard and tree level improved Symanzik actions.

hep-lat↗

arXiv1994

Heating and small-size instantons in the $O(3) \:σ$ model on the lattice

We study the role of small-size instantons in the determination of the topological susceptibility of the 2-d $O(3) \: σ$ model on the lattice. In particular, we analyze how they affect the non-perturbative determination, by Monte Carlo techniques, of the renormalizations on the lattice. As a result, we obtain a high-precision non-perturbative determination of the mixing with the unity operator, finding good agreement with perturbative computations. We also obtain the size distribution of instantons in the physical vacuum up to very small values of the size in physical units, without observing any ultraviolet cut-off. Moreover, we show by analytical calculation that the mixing of the topological susceptibility with the action density is a negligible part of the whole non-perturbative signal.

hep-lat↗