Scaling and topology in the 2-d O(3) $\sigma$-model on the lattice with the fixed point action

Abstract

We study scaling properties and topological aspects of the 2--d O(3) non--linear $\sigma$--model on the lattice with the parametrized fixed point action recently proposed by P.~Hasenfratz and F.~Niedermayer. The behavior of the mass gap confirms the good properties of scaling of the fixed point action. Concerning the topology, lattice classical solutions are proved to be very stable under local minimization of the action; this outcome ensures the reliability of the cooling method for the computation of the topological susceptibility, which indeed reproduces the results of the field theoretical approach. Disagreement is instead observed with a different approach in which the fixed point topological charge operator is used: we argue that the discrepancy is related to the ultraviolet dominated nature of the model.

arXiv comment24 pages (Latex) + 8 figures (PostScript) in a uuencoded compressed tar file

References in corpus (6)

• Perfect lattice action for asymptotically free theories
• The classically perfect fixed point action for SU(3) gauge theory
• Non--perturbative tests of the fixed point action for SU(3) gauge theory
• The absence of cut--off effects for the fixed point action in 1--loop perturbation theory
• Heating and small-size instantons in the $O(3)\sigma$ model on the lattice
• Instanton size distribution in O(3)

Cited by in corpus (9)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model
• Instantons and Fixed Point Actions in SU(2) Gauge Theory
• Renormalization group flow and fixed point of the lattice topological charge in the 2-d O(3) sigma-model
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• The clash of positivities in topological density correlators
• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
• Iterating Block Spin Transformations of the O(3) Non-Linear Sigma-Model
• Topological charge on the lattice: a field theoretical view of the geometrical approach