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

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

1994-07-29

arxiv.org/abs/hep-lat/9407026v1

Nucl.Phys.B431:686-708,1994

Physics

High Energy Physics

High Energy Physics - Lattice

41 pages, report no. IFUP-TH 42/94

Scientific paper

10.1016/0550-3213(94)90219-4

We study the role of small-size instantons in the determination of the topological susceptibility of the 2-d $O(3) \: \sigma $ 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.

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