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

Abstract

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.

arXiv comment41 pages, report no. IFUP-TH 42/94

References in corpus (3)

• Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory
• Topological susceptibility and string tension in the lattice CP(N) models
• Instanton size distribution in O(3)

Cited by in corpus (18)

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• Topology at zero and finite T in SU(2) Yang-Mills theory
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• A critical comparison of different definitions of topological charge on the lattice
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• Scaling and topology in the 2-d O(3) $\sigma$-model on the lattice with the fixed point action
• Topological Susceptibility of the 2d O(3) Model under Gradient Flow
• Testing the heating method with perturbation theory
• Analysis of systematic errors in the calculation of renormalization constants of the topological susceptibility on the lattice
• The 2-dimensional non-linear sigma-model on a random latice
• Topological Susceptibility under Gradient Flow
• Topological susceptibility through the deconfining phase transition