Topological Charge Distribution and CP1 Model with   Term

Hassan, Ahmed S.; Imachi, Masahiro; Tsuzuki, Norimasa; Yoneyama, Hiroshi

doi:10.1143/ptp.95.175

Cited by 12 publications

(12 citation statements)

References 16 publications

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“…This is useful for reducing the error in P (Q). Accordingly, the error is computed as 4) ∆P (Q) ∼ δP (Q) × P (Q), (2 . 4) where δP (Q) is almost independent of Q.…”

Section: )-5)mentioning

confidence: 99%

Maximum Entropy Method Approach to the Term

Imachi¹,

Shinno²,

Yoneyama³

2004

Progress of Theoretical Physics

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In Monte Carlo simulations of lattice field theory with a θ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution P (Q). This procedure, however, causes flattening phenomenon of the free energy f (θ), which makes study of the phase structure unfeasible. In order to treat this problem, we apply the maximum entropy method (MEM) to a Gaussian form of P (Q), which serves as a good example to test whether the MEM can be applied effectively to the θ term. We study the case with flattening as well as that without flattening. In the latter case, the results of the MEM agree with those obtained from the direct application of the Fourier transform. For the former, the MEM gives a smoother f (θ) than that of the Fourier transform. Among various default models investigated, the images which yield the least error do not show flattening, although some others cannot be excluded given the uncertainty related to statistical error. * )

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“…This is useful for reducing the error in P (Q). Accordingly, the error is computed as 4) ∆P (Q) ∼ δP (Q) × P (Q), (2 . 4) where δP (Q) is almost independent of Q.…”

Section: )-5)mentioning

confidence: 99%

Maximum Entropy Method Approach to the Term

Imachi¹,

Shinno²,

Yoneyama³

2004

Progress of Theoretical Physics

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“…The form of P t (Q) is chosen to be 10) where α and γ are adjusted so that P (Q) becomes almost flat, in order to reduce errors. The power γ is often chosen to be 2.0 (the Gaussian case).…”

Section: Definition and Algorithmmentioning

confidence: 99%

CPN-1 Models with a Term and Fixed Point Action

Burkhalter

Imachi

Shinno

et al. 2001

Progress of Theoretical Physics

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The topological charge distribution P (Q) is calculated for lattice 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 (θ) as a function of the θ parameter. For N=4, scaling behavior is observed for P (Q) and F (θ), as well as the correlation lengths ξ(Q). For N=2, however, scaling behavior is not observed, as expected. For comparison, we also make a calculation for the CP 3 model with a standard action. We furthermore pay special attention to the behavior of P (Q) in order to investigate the dynamics of instantons. For this purpose, we carefully consider the behavior of γ eff , which is an effective power of P (Q) (∼ exp(−CQ γ eff )), and reflects the local behavior of P (Q) as a function of Q. We study γ eff for two cases, the dilute gas approximation based on the Poisson distribution of instantons and the Debye-Hückel approximation of instanton quarks. In both cases, we find behavior similar to that observed in numerical simulations. §1. IntroductionIt is interesting to study the phase structure of asymptotic free theories such as QCD and the CP N −1 model. Non-perturbative studies of the phase structure of such theories are necessary in order to understand why effects of the topological term (θ term) are suppressed in Nature. The θ term affects the dynamics at low energy and is expected to lead to rich phase structures. 1) Actually, in the Z(N) gauge model, it has been shown by use of free energy arguments that oblique confinement phases could emerge and that an interesting phase structure may be realized. 2) In this paper we are concerned with the dynamics of the θ vacuum of CP N −1 models with a topological term, which have several dynamical properties in common with QCD. We believe that study of the two-dimensional model will be useful in acquiring information about realistic physics.From the numerical point of view, the topological term introduces a complex Boltzmann weight in the Euclidean lattice path integral formalism. The complex nature of the weight prevents one from straightforwardly applying the standard algorithm used for Monte Carlo simulations. This problem can be circumvented * )

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“…[47,48] There is a simple physical picture of why a limiting θ b arises. Current methods for simulating a system with θ = 0 are done using the θ = 0 system.…”

Section: Remarksmentioning

confidence: 99%