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

TL;DR

This paper compares various cooling techniques in 2D CP(N-1) lattice models, demonstrating their equivalence in analyzing topological properties and calculating topological susceptibility.

Contribution

It provides a critical comparison of cooling methods, showing their consistent behavior on classical and thermal configurations in 2D CP(N-1) models.

Findings

Cooling methods behave equivalently on classical instantons

Cooling techniques yield consistent topological susceptibility results

Cooling is validated as a reliable tool for topological studies

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.