Reliability of the optimized perturbation theory in the 0-dimensional O(N) scalar field model

Dérick S. Rosa; R.L.S. Farias; Rudnei O. Ramos

doi:10.1016/j.physa.2016.07.067

journal article Open Access Dec 01, 2016

Reliability of the optimized perturbation theory in the 0-dimensional O(N) scalar field model

Dérick S. Rosa R.L.S. Farias Rudnei O. Ramos

Physica A: Statistical Mechanics and its Applications Vol. 464 pp. 11-26 · Elsevier BV

View at Publisher Save 10.1016/j.physa.2016.07.067

Topics

No keywords indexed for this article. Browse by subject →

References

52

[1]

Gross "QCD and instantons at finite temperature" Rev. Modern Phys. (1981) 10.1103/revmodphys.53.43

[2]

Espinosa "On the phase transition in the scalar theory" Phys. Lett. B (1992) 10.1016/0370-2693(92)90129-r

[3]

Gleiser "Thermal fluctuations and validity of the one loop effective potential" Phys. Lett. B (1993) 10.1016/0370-2693(93)90365-o

[4]

Moshe "Quantum field theory in the large N limit: A Review" Phys. Rep. (2003) 10.1016/s0370-1573(03)00263-1

[5]

Okopinska "Nonstandard expansion techniques for the effective potential in lambda Phi**4 quantum field theory" Phys. Rev. D (1987) 10.1103/physrevd.35.1835

[6]

Gandhi "δ expansion of models with chiral-symmetry breaking" Phys. Rev. D (1992) 10.1103/physrevd.46.2570

[7]

Yamada "Spontaneous symmetry breaking in QCD" Z. Phys. C (1993) 10.1007/bf01555840

[8]

Klimenko "Nonlinear optimized expansions and the Gross-Neveu model" Z. Phys. C (1993) 10.1007/bf01558396

[9]

Kneur "Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem" Phys. Rev. A (2003) 10.1103/physreva.68.043615

[10]

Pinto "Evaluating critical exponents in the optimized perturbation theory" Physica A (2004) 10.1016/j.physa.2004.05.042

[11]

Farias "Applicability of the linear δ expansion for the λϕ4 field theory at finite temperature in the symmetric and broken phases" Phys. Rev. D (2008) 10.1103/physrevd.78.065046

[12]

Farias "Reliability of the optimized perturbation theory for scalar fields at finite temperature" AIP Conf. Proc. (2013) 10.1063/1.4795989

[13]

Duarte "Non-perturbative description of self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field" AIP Conf. Proc. (2013) 10.1063/1.4795995

[14]

Farias "Bulk viscosity in optimized perturbation theory" AIP Conf. Proc. (2010) 10.1063/1.3523218

[15]

Abdalla "An extension of the linear delta expansion to superspace" Phys. Rev. D (2008) 10.1103/physrevd.77.125020

[16]

Duarte "Optimized perturbation theory for charged scalar fields at finite temperature and in an external magnetic field" Phys. Rev. D (2011) 10.1103/physrevd.84.083525

[17]

Abdalla "Supergraph approach in a higher-order linear delta expansion calculation of the effective potential for F-type broken supersymmetry" Phys. Rev. D (2012) 10.1103/physrevd.86.085024

[18]

Chiku "Optimized perturbation theory at finite temperature" Phys. Rev. D (1998) 10.1103/physrevd.58.076001

[19]

Chiku "Optimized perturbation theory at finite temperature: Two loop analysis" Progr. Theoret. Phys. (2000) 10.1143/ptp.104.1129

[20]

Braaten "Convergence of the linear δ expansion in the critical O(N) field theory" Phys. Rev. Lett. (2002) 10.1103/physrevlett.89.271602

[21]

Kleinert "Convergence behavior of variational perturbation expansion - a method for locating Bender-Wu singularities" Phys. Lett. A (1995) 10.1016/0375-9601(95)00521-4

[22]

Kleinert "Strong-coupling behavior of φ4 theories and critical exponents" Phys. Rev. D (1998) 10.1103/physrevd.57.2264

[23]

Feynman "Effective classical partition functions" Phys. Rev. A (1986) 10.1103/physreva.34.5080

[24]

Yukalov "Theory of perturbations with a strong interaction" Moscow Univ. Phys. Bull. (1976)

[25]

Yukalov "Self-similar perturbation theory" Ann. Phys. (1999) 10.1006/aphy.1999.5953

[26]

Buckley "Proof of the convergence of the linear δ expansion: Zero dimensions" Phys. Rev. D (1993) 10.1103/physrevd.47.2554

[27]

Bender "Convergence of the optimized δ expansion for the connected vacuum amplitude: Zero dimensions" Phys. Rev. D (1994) 10.1103/physrevd.49.4219

[28]

Arvanitis "Convergence of the optimized δ expansion for the connected vacuum amplitude: Anharmonic oscillator" Phys. Rev. D (1995) 10.1103/physrevd.52.3704

[29]

Andersen "Screened perturbation theory to three loops" Phys. Rev. D (2001) 10.1103/physrevd.63.105008

[30]

Braaten Phys. Rev. D (1992) 10.1103/physrevd.45.r1827

[31]

Andersen Ann. Physics (2005) 10.1016/j.aop.2004.09.017

[32]

Stevenson "Optimized perturbation theory" Phys. Rev. D (1981) 10.1103/physrevd.23.2916

[33]

Krein "Optimized delta expansion for the Walecka model" Phys. Lett. B (1996) 10.1016/0370-2693(95)01578-7

[34]

Kneur "Critical and tricritical points for the massless 2D Gross-Neveu model beyond large N" Phys. Rev. D (2006) 10.1103/physrevd.74.125020

[35]

Kneur "Updating the phase diagram of the Gross-Neveu model in 2+1 dimensions" Phys. Lett. B (2007) 10.1016/j.physletb.2007.10.013

[36]

Kneur "Thermodynamics and phase structure of the two-flavor Nambu–Jona-Lasinio model beyond large-Nc" Phys. Rev. C (2010) 10.1103/physrevc.81.065205

[37]

Pinto "High temperature resummation in the linear delta expansion" Phys. Rev. D (1999) 10.1103/physrevd.60.105005

[38]

Pinto "A nonperturbative study of inverse symmetry breaking at high temperatures" Phys. Rev. D (2000) 10.1103/physrevd.61.125016

[39]

Kneur "αS from Fπ and renormalization group optimized perturbation theory" Phys. Rev. D (2013) 10.1103/physrevd.88.074025

[40]

Kneur "Renormalization group optimized perturbation theory at finite temperatures" Phys. Rev. D (2015)

[41]

Kneur "Scale invariant resummed perturbation at finite temperatures" Phys. Rev. Lett. (2016) 10.1103/physrevlett.116.031601

[42]

Kneur "Thermodynamics and phase structure of the two-flavor Nambu–Jona-Lasinio model beyond large-Nc" Phys. Rev. C (2010) 10.1103/physrevc.81.065205

[43]

Kneur "Vector-like contributions from optimized perturbation in the abelian Nambu–Jona-Lasinio model for cold and dense quark matter" Internat. J. Modern Phys. E (2012) 10.1142/s0218301312500176

[44]

Ramond (1990)

[45]

Keitel "The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group" J. Phys. A (2012) 10.1088/1751-8113/45/10/105401

[46]

Huber "Gamma function derivation of n-sphere volumes" Amer. Math. Monthly (1982) 10.1080/00029890.1982.11995438

[47]

(1972)

[48]

Kleinert (2001)

[49]

Bellet "Convergent sequences of perturbative approximations for the anharmonic oscillator. 1. Harmonic approach" Internat. J. Modern Phys. A (1996) 10.1142/s0217751x9600256x

[50]

Kleinert "Self-similar variational perturbation theory for critical exponents" Phys. Rev. E (2005) 10.1103/physreve.71.026131

Showing 50 of 52 references

Metrics

13

Citations

52

References

Details

Published: Dec 01, 2016
Vol/Issue: 464
Pages: 11-26
License: View

Authors

Funding

Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) Award: E-26/201.424/2014

Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq Award: 475110/2013-7

Cite This Article

Dérick S. Rosa, R.L.S. Farias, Rudnei O. Ramos (2016). Reliability of the optimized perturbation theory in the 0-dimensional O(N) scalar field model. Physica A: Statistical Mechanics and its Applications, 464, 11-26. https://doi.org/10.1016/j.physa.2016.07.067

Reliability of the optimized perturbation theory in the 0-dimensional O(N) scalar field model

You May Also Like