Fixed point action and topology in the CP3model

We define a fixed point action in two-dimensional lattice $\mathrm{C}{\mathrm{P}}^{N-1\mathrm{}}$ models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cutoff effects in numerical simulations. Furthermore, the action has scale-invariant instanton solutions, which enables us to define a correct topological charge without topological defects. Using a parametrization of the fixed point action for the C${\mathrm{P}}^3$ model in a Monte Carlo simulation, we study the topological susceptibility.