Lattice CP  models and their large-N behaviour

Vecchia, P. Di; Holtkamp, Annette; Musto, R.; Nicodemi, F.; Pettorino, R.

doi:10.1016/0550-3213(81)90047-x

Cited by 54 publications

(48 citation statements)

References 27 publications

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“…In turn, all contributions to physical quantities are dominated by the lighter degrees of freedom that correspond to the continuum physics we are interested in. As a matter of fact, when comparing with the so-called standard action [5], we found precocious scaling, and for higher values of N even asymptotic scaling is observable.…”

Section: Introductionmentioning

confidence: 86%

Monte Carlo simulation ofCPN−1models

1992

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Numerical simulations of two-dimensional CpN-' models are performed at N = 2, 10, and 21. The lattice action adopted depends explicitly on the gauge degrees of freedom and shows precocious scaling. Our tests of scaling are the stability of dimensionless physical quantities (second moment of the correlation function versus inverse mass gap, magnetic susceptibility versus square correlation length) and rotation invariance. Topological properties of the models are explored by measuring the topological susceptibility and by extracting the Abelian string tension. Several different (local and nonlocal) lattice definitions of topological charge are discussed and compared. The qualitative physical picture derived from the continuum 1/N expansion is confirmed, and agreement with quantitative 1/N predictions is satisfactory. Variant (Symanzik-improved) actions are considered in the CP1 = O(3) case and agreement with universality and previous simulations (when comparable) is found. The simulation algorithm is an efficient mixture of over-heat-bath and microcanonical algorithms. The dynamical features and critical exponents of the algorithm are discussed in detail.

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Section: Introductionmentioning

confidence: 86%

Monte Carlo simulation ofCPN−1models

1992

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“…In the limit γ → ∞, the gauge link variables are all equal to one modulo gauge transformations, and the AH model becomes equivalent to the standard O(n) vector model with n = 2N . For γ = 0, corresponding to the infinite gauge-coupling limit, the AH model (1) is a particular lattice formulation of the CP N −1 model [29][30][31][32][33][34]. 2D CP N −1 models have been much studied in the literature, both analytically and numerically, because they provide a theoretical laboratory to understand some of the mechanisms of quantum field theories of fundamental interactions.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional multicomponent Abelian-Higgs lattice models

2020

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We study the two-dimensional lattice multicomponent Abelian-Higgs model, which is a lattice compact U(1) gauge theory coupled with an N -component complex scalar field, characterized by a global SU(N ) symmetry. In agreement with the Mermin-Wagner theorem, the model has only a disordered phase at finite temperature and a critical behavior is only observed in the zero-temperature limit. The universal features are investigated by numerical analyses of the finite-size scaling behavior in the zero-temperature limit. The results show that the renormalization-group flow of the 2D lattice N -component Abelian-Higgs model is asymptotically controlled by the infinite gauge-coupling fixed point, associated with the universality class of the 2D CP N−1 field theory.

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“…We consider the lattice action (8.17) which is more convenient for a large-N expansion [123,217,218]. One can easily prove that site-and link-reflection positivity holds for the lattice action (8.17).…”

Section: The Large-n Limit On the Latticementioning

confidence: 99%

“…2D CP N −1 models have also been studied by exploiting lattice techniques, based on the straighforward discretization of the continuum action [217] (in the following we set the lattice spacing a = 1) (8.16) or the lattice action [76,217,457]: 17) where β = 1/g, z n is a complex N -component vector, constrained by the conditionz n z n = 1, and λ n,µ is an auxiliary U (1) variable. The lattice CP N −1 model represents a very useful theoretical laboratory for testing the various numerical methods to determine topological properties, and in particular the topological susceptibility, also because the results can be compared with the analytic 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 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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Lattice CP models and their large-N behaviour

Cited by 54 publications

References 27 publications

Monte Carlo simulation ofCPN−1models

Monte Carlo simulation ofCPN−1models

Two-dimensional multicomponent Abelian-Higgs lattice models

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

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