Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2001-03-16
Prog.Theor.Phys. 106 (2001) 613-640
Physics
High Energy Physics
High Energy Physics - Lattice
PTPTEX.sty <ver.1.0>, 29 pages with 20 figures
Scientific paper
10.1143/PTP.106.613
The topological charge distribution P(Q) is calculated for lattice ${\rm CP}^{N-1}$ models. In order to suppress lattice cut-off effects we employ a fixed point (FP) action. Through transformation of P(Q) we calculate the free energy $F(\theta)$ as a function of the $\theta$ parameter. For N=4, scaling behavior 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. For comparison, we also make a calculation for the ${\rm CP}^{3}$ model with standard action. We furthermore pay special attention to the behavior of P(Q) in order to investigate the dynamics of instantons. For that purpose, we carefully look at behavior of $\gamma_{\it eff}$, which is an effective power of P(Q)($\sim \exp(-CQ^{\gamma_{\it eff}})$), and reflects the local behavior of P(Q) as a function of Q. We study $\gamma_{\it eff}$ for two cases, one of which is the dilute gas approximation based on the Poisson distribution of instantons and the other is the Debye-H\"uckel approximation of instanton quarks. In both cases we find similar behavior to the one observed in numerical simulations.
Burkhalter Rudolf
Imachi Masahiro
Shinno Yasuhiko
Yoneyama Hiroshi
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