The O(N) linear sigma model at finite temperature beyond the Hartree approximation

Abstract

We study the O(N) linear sigma model with spontaneous symmetry breaking, using a Hartree-like ansatz with a classical field and variational masses. We go beyond the Hartree approximation by including the two-loop contribution, the sunset diagram, using the 2PPI expansion. We have computed numerically the effective potential at finite temperature. We find a phase transition of second order, while it is first order in the Hartree approximation. We also discuss some implications of the fact that in this order, the decay of the sigma into two pions affects the thermal diagrams.

22 pages, 14 figures. v2: minor corrections, some more references. v3: added new set of data, new appendix. Submitted to Phys.Rev.D

References in corpus (35)

• Dynamics of Symmetry Breaking and Tachyonic Preheating
• Resummation in a Hot Scalar Field Theory
• Tachyonic Instability and Dynamics of Spontaneous Symmetry Breaking
• Controlled nonperturbative dynamics of quantum fields out of equilibrium
• Far-from-equilibrium dynamics with broken symmetries from the 2PI-1/N expansion
• Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations
• Nonequilibrium Dynamics of Symmetry Breaking in Lambda Phi^4 Field Theory
• Self-consistent Improvement of the Finite Temperature Effective Potential
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• Symmetry Breaking and False Vacuum Decay after Hybrid Inflation
• Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries
• Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram
• The O(N) Model at Finite Temperature: Renormalization of the Gap Equations in Hartree and Large-N Approximation
• Linear sigma model and chiral symmetry at finite temperature
• O(N) Quantum fields in curved spacetime
• Quantum dynamics of phase transitions in broken symmetry $\lambda {\varphi }^4$ field theory
• Schwinger-Dyson approach to non-equilibrium classical field theory
• Non-Equilibrium Bose-Einstein Condensates, Dynamical Scaling and Symmetric Evolution in large N Phi^4 theory
• Resumming the large-N approximation for time evolving quantum systems
• Thermal Effective Potential of the O(N) Linear sigma Model
• Effective Potential of O(N) Linear Sigma Model at Finite Temperature
• Exact and approximate dynamics of the quantum mechanical O(N) model
• Thermalization of an Interacting Quantum Field in the CTP-2PI Next-to-leading-order Large N Scheme
• Finite temperature spectral functions of the linear O(N)-model at large N applied to the $\pi -\sigma$ system
• Summation and renormalization of bubble graphs to all orders
• Study of the O(N) linear sigma model at finite temperature using the 2PPI expansion
• Nonequilibrium evolution and symmetry structure of the large-N ${\Phi }^4$ model at finite temperature
• Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking
• A 2 Loop 2PPI Analysis of $\lambda {\varphi }^4$ at Finite Temperature
• Dynamics of broken symmetry lambda phi^4 field theory
• Goldstone excitations from spinodal instability
• Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism
• Out-of-equilibrium dynamics of large-N ϕ^4 QFT in finite volume
• An improved time-dependent Hartree-Fock approach for scalar ϕ^4 QFT
• Relaxation of 2+1 dimensional classical O(2) symmetric scalar fields

Cited by in corpus (25)

• Symmetry Improved CJT Effective Action
• Gapless Hartree-Fock Resummation Scheme for the O(N) Model
• Constraining the effective action by a method of external sources
• Selfconsistent calculations of spectral densities in the O(N) model: improving the Hartree-Fock approximation by including nonzero decay widths
• Thermodynamics of O(N) sigma models: 1/N corrections
• Topological Susceptibility in Three-Flavor Quark Meson Model at Finite Temperature
• 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
• Critical Behavior and Dimension Crossover of Pion Superfluidity
• Functional renormalization group study of the critical region of the quark-meson model with vector interactions
• Role reversal in first and second sound in a relativistic superfluid
• On the symmetry improved CJT formalism in the $O(4)$ linear sigma model
• Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism
• Superfluid two-stream instability in a microscopic model
• Quantum dynamics of Phi**4 field theory beyond leading order in 1+1 dimensions
• The renormalized and Renormalization-Group invariant Hartree-Fock approximation
• The O(2) model in polar coordinates at nonzero temperature
• Finite Temperature Description of an Interacting Bose Gas
• Delaying the waterfall transition in warm hybrid inflation
• The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N
• Trapped surfaces in a hadronic fluid
• One-meson-loop NJL model: Effect of collective and noncollective excitations on the quark condensate at finite temperature
• Analogue surface gravity near the QCD chiral phase transition
• $U_A(1)$ symmetry restoration at high baryon density
• The type of the phase transition and coupling values in λϕ^4 model
• Improved Hartree--Fock resummations and spontaneous symmetry breaking