Convergence of the Linear Delta Expansion in the Critical O(N) Field Theory

Abstract

The linear delta expansion is applied to the 3-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear delta expansion for <phi^2> converges, with errors decreasing like a power of the order n in delta. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with n.

26 pages, latex, 8 figures

References in corpus (3)

• Transition temperature of a dilute homogeneous imperfect Bose gas
• T_c for homogeneous dilute Bose gases: a second-order result
• Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

Cited by in corpus (31)

• Principal problems in Bose-Einstein condensation of dilute gases
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Bose-Einstein Condensation Temperature of a Homogeneous Weakly Interacting Bose Gas : PIMC study
• A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature
• Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem
• Multiple Critical Points in Effective Quark Models
• Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N
• Critical Dopant Concentration in Polyacetylene and Phase Diagram from a Continuous Four-Fermi Model
• Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model
• Applicability of the Linear delta Expansion for the lambda phi^4 Field Theory at Finite Temperature in the Symmetric and Broken Phases
• Bose-Einstein condensation temperature of weakly interacting atoms
• A brief overview of hard-thermal-loop perturbation theory
• Nonperturbative Yukawa theory at finite density and temperature
• New Optimization Methods for Converging Perturbative Series with a Field Cutoff
• Exact 1/N and Optimized Perturbative Evaluation of mu_c for Homogeneous Interacting Bose Gases
• Mean field approach to flavor susceptibilities with a vector interaction
• Reliability of the optimized perturbation theory in the 0-dimensional $O(N)$ scalar field model
• Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory
• Condensation temperature of interacting Bose gases with and without disorder
• Interplay Between Approximation Theory and Renormalization Group
• Testing the Gaussian expansion method in exactly solvable matrix models
• A Deal with the Devil: From Divergent Perturbation Theory to an Exponentially-Convergent Self-Consistent Expansion
• From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
• Evaluating Critical Exponents in the Optimized Perturbation Theory
• $1/N$-expansion for the critical temperature of the Bose gas
• Constrained extrapolation problem and order-dependent mappings
• Supergraph Approach in a Higher-order LDE Calculation of the Effective Potential for F-type Broken SUSY