Broken phase scalar effective potential and Phi-derivable approximations

Abstract

We study the effective potential of a real scalar phi^4 theory as a function of the temperature T within the simplest Phi-derivable approximation, namely the Hartree approximation. We apply renormalization at a "high" temperature T* where the theory is required to be in its symmetric phase and study how the effective potential evolves as the temperature is lowered down to T=0. In particular, we prove analytically that no second order phase transition can occur in this particular approximation of the theory, in agreement with earlier studies based on the numerical evaluation or the high temperature expansion of the effective potential. This work is also an opportunity to illustrate certain issues on the renormalization of Phi-derivable approximations at finite temperature and non-vanishing field expectation value, and to introduce new computational techniques which might also prove useful when dealing with higher order approximations.

23 pages, 5 figures, uses revtex4

References in corpus (10)

• Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium
• Linear sigma model at finite density in the 1/N expansion to next-to-leading order
• Techniques for n-Particle Irreducible Effective Theories
• Exact renormalization group and Phi-derivable approximations
• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion
• Renormalized Finite Temperature phi^4 theory from the 2PI Effective Action
• Topological defect formation from 2PI effective action techniques
• Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields
• Counterterm resummation for 2PI-approximation in constant background

Cited by in corpus (19)

• Effective potential for quantum scalar fields on a de Sitter geometry
• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• Renormalization group flow and symmetry restoration in de Sitter space
• The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential
• Functional renormalization group and 2PI effective action formalism
• Thermodynamics and phase transition of the O(N) model from the two-loop Phi-derivable approximation
• Symmetry breaking and the Goldstone theorem in de Sitter space
• Broken phase effective potential in the two-loop Phi-derivable approximation and nature of the phase transition in a scalar theory
• Variational study of mass generation and deconfinement in Yang-Mills theory
• Non-equilibrium dynamics of a scalar field with quantum backreaction
• The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations
• Padé approximants and analytic continuation of Euclidean Phi-derivable approximations
• A critical look at the role of the bare parameters in the renormalization of Phi-derivable approximations
• Broken symmetry phase solution of the phi^4 model at two-loop level of the Phi-derivable approximation
• Renormalized O(N) model at next-to-leading order of the 1/N expansion: Effects of the Landau pole
• Renormalization of the 2PI-Hartree approximation in a broken phase with nonzero superflow
• nPI Resummation in 3D SU(N) Higgs Theory