Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory

Abstract

Perturbation theory, as well as most thermal field resummation methods widely used to study finite-temperature quantum field theories, presents a non-negligible renormalization scale dependence. To address this limitation, we propose an alternative method that combines the renormalization group improvement prescription for the thermal effective potential with the optimized perturbation theory variational resummation technique. Here, we apply this new framework, termed variational renormalization group, to evaluate the effective potential of the scalar $\lambda {\varphi }^4$ theory at finite temperatures, which represents a benchmark model for phase transition studies. We show that the proposed approach significantly improves scale stability, compared to the use of optimized perturbation theory alone, across key thermodynamic quantities, including the effective potential, critical temperature, and pressure. These results establish the variational renormalization group as a robust alternative tool for precision studies of thermal phase transitions, with direct implications for cosmological applications (e.g., early-Universe thermodynamics) and condensed matter systems.

arXiv comment19 pages, 8 figures. Replaced with the version matching the one published in the PRD

References in corpus (53)

• Resummation in a Hot Scalar Field Theory
• The effective potential and the renormalisation group
• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• Theoretical uncertainties for cosmological first-order phase transitions
• Resummation in Hot Field Theories
• Three-loop HTL QCD thermodynamics
• Renormalization Group Improvement of the Effective Potential in Massive O(N) Symmetric ${\varphi }^4$ Theory
• Five-loop renormalization group functions of $O(n)$-symmetric ${\varphi }^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$
• Improving the Effective Potential
• Screened Perturbation Theory to Three Loops
• Three-loop HTLpt Pressure and Susceptibilities at Finite Temperature and Density
• On the perturbative expansion at high temperature and implications for cosmological phase transitions
• Equation of State of hot and dense QCD: Resummed perturbation theory confronts lattice data
• Gluon Thermodynamics at Intermediate Coupling
• Improving the Effective Potential:Multi-Mass-Scale Case
• A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Transition Temperature for Weakly Interacting Homogeneous Bose Gases
• Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
• Convergent resummed linear delta expansion in the critical O(N) (ϕ_i^2)^2_{3d} model
• Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c
• Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions
• High Temperature Resummation in the Linear $\delta$-Expansion
• Magnetization of Planar Four-Fermion Systems
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• Optimized perturbation theory for charged scalar fields at finite temperature and in an external magnetic field
• Real scalar phase transitions: a nonperturbative analysis
• Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model
• The Massive Thermal Basketball Diagram
• Critical Dopant Concentration in Polyacetylene and Phase Diagram from a Continuous Four-Fermi Model
• The chiral condensate from renormalization group optimized perturbation
• 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
• A Multi-scale Subtraction Scheme and Partial Renormalization Group Equations in the $O(N)$-symmetric ${\varphi }^4$-theory
• Dynamical Generation of a Repulsive Vector Contribution to the Quark Pressure
• Multi-scale Renormalisation Group Improvement of the Effective Potential
• A brief overview of hard-thermal-loop perturbation theory
• Renormalization Group Optimized Perturbation Theory at Finite Temperatures
• Scale Invariant Resummed Perturbation at Finite Temperatures
• Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group
• Broken phase effective potential in the two-loop Phi-derivable approximation and nature of the phase transition in a scalar theory
• Renormalization group improvement of the effective potential in massive ${\varphi }^4$ theory
• Stop comparing resummation methods
• Thermodynamics of Quasi-Particles
• Reliability of the optimized perturbation theory in the 0-dimensional $O(N)$ scalar field model
• Vector-like contributions from Optimized Perturbation in the Abelian Nambu--Jona-Lasinio model for cold and dense quark matter
• Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu--Jona-Lasinio model
• Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order
• Comparing strange and non-strange quark stars within resummed QCD at NLO
• First order phase transitions within Weyl type of materials at low temperatures
• Phase transition patterns for coupled complex scalar fields at finite temperature and density
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Charged scalars at finite electric field and temperature in the optimized perturbation theory