Four-point renormalized coupling constant in O(N) models

Campostrini, Massimo; Pelissetto, Andrea; Rossi, Paolo; Vicari, Ettore

doi:10.1016/0920-5632(96)00166-1

Cited by 11 publications

(18 citation statements)

References 13 publications

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“…Note that N does not play any role here, thus the critical behavior does not depend on N . It is natural to conjecture that the same behavior holds[61] allow us to obtain Jc(κ → ∞) = b∞ + b∞,1N −1 + O(N −2 ), with b∞ = 0.252731... and b∞,1 ≈ −0.0585.…”

mentioning

confidence: 76%

“…We also report the nature of the transition: FO and O(n) indicate a first-order transition and a continuous transition in the O(n) vector universality class, respectively. The estimates of Jc for κ → ∞ for 7 ≤ N ≤ 20 are obtained by interpolating the results of Ref [61]. for the lattice O(n) vector model (the uncertainty on these interpolations is safely below 1 on the last reported digit).…”

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confidence: 99%

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Lattice Abelian-Higgs model with noncompact gauge fields

Bonati,

Pelissetto,

Vicari

2020

Preprint

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confidence: 76%

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confidence: 99%

Lattice Abelian-Higgs model with noncompact gauge fields

Bonati,

Pelissetto,

Vicari

2020

Preprint

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“…Specifically in sigma-models with a compact global symmetry group the expansion is known to be an asymptotic expansion [1] and when slightly ad hoc applied to low orders at fixed small N sometimes gives surprisingly accurate results, see e.g. [2,3] for the renormalized coupling. In a lattice formulation one starts off on a finite lattice, the associated 'finite volume' mass gap then is uniformly bounded away from zero, and in the large N series for invariant correlation functions the limit of infinite lattice size (also called the thermodynamic limit) can safely be taken termwise.…”

Section: Introductionmentioning

confidence: 99%

Noncompact sigma-models: Large N expansion and thermodynamic limit

2008

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Noncompact SO(1, N) sigma-models are studied in terms of their large N expansion in a lattice formulation in dimensions d ≥ 2. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented to next to leading order on a finite lattice. The dynamically generated gap is negative and serves as a coupling-dependent infrared regulator which vanishes in the limit of infinite lattice size. The cancellation of infrared divergences in invariant correlation functions in this limit is nontrivial and is in d = 2 demonstrated by explicit computation for the above quantities. For the Binder cumulant the thermodynamic limit is finite and is given by 2/(N +1) in the order considered. Monte Carlo simulations suggest that the remainder is small or zero. The potential implications for "criticality" and "triviality" of the theories in the SO(1, N) invariant sector are discussed. * Membre du CNRS

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“…We thus recover the O(2N ) vector model. For N = 2 the relevant model is the O(4) model, which has a transition at [38][39][40] J c = 0.233965 (2). Estimates of the O(4) critical exponents can be found in Refs.…”

Section: Phase Diagram and Critical Behaviorsmentioning

confidence: 99%

Lattice gauge theories in the presence of a linear gauge-symmetry breaking

Bonati,

Pelissetto,

Vicari

2021

Preprint

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We study the effects of gauge-symmetry breaking (GSB) perturbations in three-dimensional lattice gauge theories with scalar fields. We study this issue at transitions in which gauge correlations are not critical and the gauge symmetry only selects the gauge-invariant scalar degrees of freedom that become critical. A paradigmatic model in which this behavior is realized is the lattice CP 1 model or, more generally, the lattice Abelian-Higgs model with two-component complex scalar fields and compact gauge fields. We consider this model in the presence of a linear GSB perturbation. The gauge symmetry turns out to be quite robust with respect to the GSB perturbation: the continuum limit is gauge-invariant also in the presence of a finite small GSB term. We also determine the phase diagram of the model. It has one disordered phase and two phases that are tensor and vector ordered, respectively. They are separated by continuous transition lines, which belong to the O(3), O(4), and O(2) vector universality classes, and which meet at a multicritical point. We remark that the behavior at the CP 1 gauge-symmetric critical point substantially differs from that at transitions in which gauge correlations become critical, for instance at transitions in the noncompact lattice Abelian-Higgs model that are controlled by the charged fixed point: in this case the behavior is extremely sensitive to GSB perturbations.

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Four-point renormalized coupling constant in O(N) models

Cited by 11 publications

References 13 publications

Lattice Abelian-Higgs model with noncompact gauge fields

Lattice Abelian-Higgs model with noncompact gauge fields

Noncompact sigma-models: Large N expansion and thermodynamic limit

Lattice gauge theories in the presence of a linear gauge-symmetry breaking

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