Monte Carlo studies of two-dimensional systems with a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>θ</mml:mi></mml:math>term

Plefka, Jan; Samuel, Stuart

doi:10.1103/physrevd.56.44

Cited by 32 publications

(53 citation statements)

References 47 publications

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“…Refs. [38,54,56,59,70,89,114,350,437,450,451,475]. Like 4D SU (N ) gauge theories, the Euclidean action with the θ term is complex, which impedes a Monte Carlo simulation of the theory using its straightforward discretization, i.e.…”

Section: Results Around θ = πmentioning

confidence: 99%

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θ dependence of SU(N) gauge theories in the presence of a topological term

2009

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We review results concerning the θ dependence of 4D SU (N ) gauge theories and QCD, where θ is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we discuss θ dependence in the large-N limit.Most results have been obtained within the lattice formulation of the theory via numerical simulations. We review results at zero and finite temperature. We show that the results support the scenario obtained by general large-N scaling arguments, and in particular the Witten-Veneziano mechanism to explain the U (1) A problem. We also compare with results obtained by other approaches, especially in the large-N limit, where the issue has been also addressed using, for example, the AdS/CFT correspondence.We discuss issues related to theta dependence in full QCD: the neutron electric dipole moment, the dependence of the topological susceptibility on the quark masses, the U (1) A symmetry breaking at finite temperature.We also review results in the 2D CP N −1 model, which is an interesting theoretical laboratory to study issues related to topology.Finally, we discuss the main features of the two-point correlation function of the topological charge density.

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Section: Results Around θ = πmentioning

confidence: 99%

“…[29,55,70,75,77,95,113,114,124,125,193,201,202,299,331,338,350,374,393,450,451,458,475,533,535,554]. A wide range of values of N has been considered, both small and large, in order to test large-N calculations.…”

Section: Lattice Calculations At θ =mentioning

confidence: 99%

θ dependence of SU(N) gauge theories in the presence of a topological term

2009

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“…We obtain smooth curves, and no "flattening" is observed, as in some other works. 11), 18), 19) The only exception is the simulation with L = 96 (not shown in the figure), where the calculation of F (θ) breaks down at θ ≈ 1, because the partition function turns out to be negative (while still consistent with zero within the error bars). Before this breakdown, the error bars become very large.…”

Section: Free Energy Density and Expectation Value Of The Topologicalmentioning

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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“…In fact, a fictitious signal of a phase transition was observed due to the errors of P (Q) [ 5,6]. This is called flattening.…”

Section: Introductionmentioning

confidence: 99%

Application of maximum entropy method to lattice field theory with a topological term

Imachi

Shinno

Yoneyama

2004

Nuclear Physics B - Proceedings Supplements

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In Monte Carlo simulation, lattice field theory with a θ term suffers from the sign problem. This problem can be circumvented by Fourier-transforming the topological charge distribution P (Q). Although this strategy works well for small lattice volume, effect of errors of P (Q) becomes serious with increasing volume and prevents one from studying the phase structure. This is called flattening. As an alternative approach, we apply the maximum entropy method (MEM) to the Gaussian P (Q). It is found that the flattening could be much improved by use of the MEM.

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Monte Carlo studies of two-dimensional systems with aθterm

Cited by 32 publications

References 47 publications

θ dependence of SU(N) gauge theories in the presence of a topological term

θ dependence of SU(N) gauge theories in the presence of a topological term

CPN-1 Models with a Term and Fixed Point Action

Application of maximum entropy method to lattice field theory with a topological term

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