CPN-1 Models with a Term and Fixed Point Action

The topological charge distribution P(Q) is calculated for lattice ${\rmCP}^{N-1}$ models. In order to suppress lattice cut-off effects we employ afixed point (FP) action. Through transformation of P(Q) we calculate the freeenergy $F(\theta)$ as a function of the $\theta$ parameter. For N=4, scalingbehavior is observed for P(Q), $F(\theta)$ as well as the correlation lengths$\xi(Q)$. For N=2, however, scaling behavior is not observed as expected. Forcomparison, we also make a calculation for the ${\rm CP}^{3}$ model withstandard action. We furthermore pay special attention to the behavior of P(Q)in order to investigate the dynamics of instantons. For that purpose, wecarefully look at behavior of $\gamma_{\it eff}$, which is an effective powerof P(Q)($\sim \exp(-CQ^{\gamma_{\it eff}})$), and reflects the local behaviorof P(Q) as a function of Q. We study $\gamma_{\it eff}$ for two cases, one ofwhich is the dilute gas approximation based on the Poisson distribution ofinstantons and the other is the Debye-H\"uckel approximation of instantonquarks. In both cases we find similar behavior to the one observed in numericalsimulations.Comment: PTPTEX.sty , 29 pages with 20 figure