Topology in 2D CP**(N-1) models on the lattice: a critical comparison of different cooling techniques

Abstract

Two-dimensional CP**(N-1) models are used to compare the behavior of different cooling techniques on the lattice. Cooling is one of the most frequently used tools to study on the lattice the topological properties of the vacuum of a field theory. We show that different cooling methods behave in an equivalent way. To see this we apply the cooling methods on classical instantonic configurations and on configurations of the thermal equilibrium ensemble. We also calculate the topological susceptibility by using the cooling technique.

24 pages, 10 figures (from 16 eps files)

References in corpus (7)

• Topological Structure of the SU(3) Vacuum
• Confronting Instanton Perturbation Theory with QCD Lattice Results
• Cooling, Physical Scales and Topology
• Topology at zero and finite T in SU(2) Yang-Mills theory
• Smeared Gauge Fixing
• On Statistical Mechanics of Instantons in the CP^{N_c-1} Model
• The topological susceptibility of QCD: from Minkowskian to Euclidean theory

Cited by in corpus (18)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Comparison of the gradient flow with cooling in $SU(3)$ pure gauge theory
• Critical slowing down of topological modes
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• Behaviour of the topological susceptibility in two colour QCD across the finite density transition
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
• Ground state modulations in the $\mathbb{C}{P}^{N-1}$ model
• Two-dimensional multicomponent Abelian-Higgs lattice models
• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
• Remarks on the large-$N$ $\mathbb{C}{P}^{N-1}$ model
• Comparison of smoothening flows for the topological charge in QCD-like theories
• Analysis of systematic errors in the calculation of renormalization constants of the topological susceptibility on the lattice
• Yang--Mills topology on four-dimensional triangulations