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

Abstract

We address the reliability of the Optimized Perturbation Theory (OPT) in the context of the 0-dimensional $O(N)$ scalar field model. The effective potential, the self-energy and the 1PI four-point Green's function for the model are computed using different optimization schemes and the results contrasted to the exact results for the model. Our results are also compared to those obtained with the $1/N$-expansion and with those from ordinary perturbation theory. The OPT results are shown to be stable even at large couplings and to have better convergence properties than the ones produced in the $1/N$-expansion. It is also shown that the principle of minimal sensitive optimization procedure used in conjunction with the OPT method tends to always produce better results, in particular when applied directly to the self-energy.

38 pages, 13 figures, v2 Physica A version

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Cited by in corpus (13)

• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Interplay Between Approximation Theory and Renormalization Group
• Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu--Jona-Lasinio model
• A Deal with the Devil: From Divergent Perturbation Theory to an Exponentially-Convergent Self-Consistent Expansion
• Polyakov linear-sigma model in mean-field approximation and optimized perturbation theory
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Phase transition patterns for coupled complex scalar fields at finite temperature and density
• Charged scalars at finite electric field and temperature in the optimized perturbation theory
• Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory
• Symmetry breaking patterns for two coupled complex scalar fields at finite temperature and in an external magnetic field