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

TL;DR

This paper investigates the scaling and topological features of the 2D O(3) sigma model on the lattice using a fixed point action, confirming good scaling behavior and reliable topological measurements, while highlighting discrepancies with alternative methods.

Contribution

It demonstrates the stability of lattice classical solutions and validates the cooling method for topological susceptibility, addressing discrepancies with other approaches.

Findings

Mass gap confirms good scaling properties.

Cooling method reliably computes topological susceptibility.

Discrepancies with fixed point topological charge operator are linked to ultraviolet effects.

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.