Erratum: Renormalization-group picture of the Lifshitz critical behavior [Phys. Rev. B<b>67</b>, 104415 (2003)]

Leite, Marcelo M.

doi:10.1103/physrevb.80.029904

Cited by 17 publications

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“…Even at low energies, if we want to study phase transitions and critical phenomena using perturbative field-theoretical methods, for example for Lifshitz points, we have to renormalize LV theories as well [14][15][16][17]. In this case, the breaking of Lorentz symmetry is easily seen through the free propagator of the theory whose dispersion relation is not quadratic.…”

Section: Introductionmentioning

confidence: 99%

Mass renormalization in Lorentz-violating scalar field theory

Carvalho¹

2013

Physics Letters B

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Section: Introductionmentioning

confidence: 99%

Mass renormalization in Lorentz-violating scalar field theory

Carvalho¹

2013

Physics Letters B

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“…Finite-systems with Lifshitz bulk critical behavior could be studied within this new paradigm. This would allow the computation of universal quantities like critical exponents [31][32][33][34] and amplitude ratios [35][36][37][38]. Ferroelectric materials exhibit Lifshitz bulk behavior.…”

Section: Discussionmentioning

confidence: 99%

Neumann boundary conditions with null external quasi-momenta in finite systems

2019

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The order parameter of a critical system defined in a layered parallel plate geometry subject to Neumann boundary conditions at the limiting surfaces is studied. We utilize a one-particle irreducible vertex parts framework in order to study the critical behavior of such a system. The renormalized vertex parts are defined at zero external quasi-momenta, which makes the analysis particularly simple. The distance between the boundary plates L characterizing the finite size system direction perpendicular to the hyperplanes plays a similar role here in comparison with our recent unified treatment for Neumann and Dirichlet boundary conditions. Critical exponents are computed using diagrammatic expansion at least up to two-loop order and are shown to be identical to those from the bulk theory (limit L → ∞).

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“…Furthermore, the present exact approach, when applied to the referred theory, is the first one in literature for our knowledge. Thus it can inspire the exact solution of problems involving considering the exact effect of LV mechanisms in many physical phenomena ranging from high-(standard model extension for example) to low energy physics (corrections to scaling, finite-size scaling, amplitude ratios, critical exponents in geometries subjected to different boundary conditions, Lifshitz points etc [29][30][31][32].…”

Section: Discussionmentioning

confidence: 99%

Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories

Carvalho

Sena-Junior

2017

Eur. Phys. J. C

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In this work we evaluate analytically the ultraviolet divergences of Lorentz-violating massive O(N ) λφ 4 scalar field theories, which are exact in the Lorentz-violating mechanism, firstly explicitly at next-to-leading order and latter at any loop level through an induction procedure based on a theorem following from the exact approach, for computing the corresponding critical exponents. For attaining that goal, we employ three different and independent field-theoretic renormalization group methods. The results found for the critical exponents show that they are identical in the three distinct methods and equal to their Lorentz-invariant counterparts. Furthermore, we show that the results obtained here, based on the single concept of loop order of the referred terms of the corresponding β-function and anomalous dimensions, reduce to the ones obtained through the earlier non-exact approach based on a joint redefinition of the field and coupling constant of the theory, in the appropriate limit.

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Erratum: Renormalization-group picture of the Lifshitz critical behavior [Phys. Rev. B67, 104415 (2003)]

Cited by 17 publications

References 0 publications

Mass renormalization in Lorentz-violating scalar field theory

Mass renormalization in Lorentz-violating scalar field theory

Neumann boundary conditions with null external quasi-momenta in finite systems

Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories

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