Topology in CPN−1 models: a critical comparison of different cooling techniques

Two-dimensional CPN−1 models play an important role in quantum field theory because they share many properties with QCD. In particular, they possess instanton classical solutions and one can define topological charge and susceptibility in analogy with QCD. CPN−1 models represent therefore a useful theoretical laboratory to investigate numerical methods to be eventually applied to study the topology in QCD. One of the most powerful tools for the study of the topological structure of the vacuum is the “cooling” method. It consists in measuring the topologically relevant quantities on the ensemble of lattice configurations obtained by replacing each equilibrium configuration by the one resulting after a sequence of local minimizations of the action. The aim of this work is to get insight into a new cooling method first adopted in Ref. [1], by comparing it with the “standard” [2] and with its “controlled” version adopted by the Pisa group [3]. We chose the standard discretization for the action of the 2d CPN−1 model: S =−Nβ ∑