<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>linear sigma model at finite temperature beyond the Hartree approximation

Baacke, J.; Michalski, Stefan

doi:10.1103/physrevd.67.085006

Cited by 40 publications

(47 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, for the case of global O(N ) symmetries that we will be studying here, a naive truncation of the CJT effective action violates the Goldstone theorem [7,8] by higher-order terms, giving rise to a massive Goldstone boson in the Spontaneous Symmetry Breaking (SSB) phase of the theory [9][10][11][12]. Thus far, several studies have been presented in the literature, attempting to provide a satisfactory solution to this problem [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…It predicts a sequence of two second-order phase transitions, including an unnatural symmetric phase of the theory, in which the masses of the Goldstone and Higgs particles are different, even though the vacuum expectation value (VEV) of the background field vanishes. Another approach employs a Two-Point-ParticleIrreducible effective action [15], but the Goldstone boson turns out to be massive at the next-to-leading order in a 1/N expansion.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry-improved CJT effective action

2013

View full text Add to dashboard Cite

The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward identities due to global symmetries. By considering a simple O(2) scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O (2) is massless and the phase transition is a second order one, already in the Hartree-Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree-Fock approximated CJT effective action, we calculate the corresponding symmetryimproved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetry-improved CJT effective action

2013

View full text Add to dashboard Cite

show abstract

“…In these cases, the gap equations for the propagators are easy to solve since the self-energy reduces to a local mass term. In the Hartree approximation, the result has been shown to be problematic (and a first-order phase transition occurs), which has been remedied by including more diagrams in the truncation [17,18], resulting in a second-order phase transition. If one goes beyond the Hartree approximation or includes the NLO contributions in the 1/N expansion, the gap equations become nonlocal and very difficult to solve.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics ofO(N)sigma models:1/Ncorrections

2004

View full text Add to dashboard Cite

The thermodynamics of the O(N ) linear and nonlinear sigma models in 3+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, temperature-independent renormalization is only possible at the minimum of the effective potential. The 1/N expansion is found to be a good expansion for N as low as 4, which is the case relevant for low-energy QCD phenomenology. We consider the cases with and without explicit symmetry breaking. We show that previous next-to-leading order calculations of the pressure are either breaking down in the temperatures of interest, or based on unjustifiable high-energy approximations.

show abstract

“…In Ref. [5] a second order phase transition for the O(N)-model was determined independently of the coupling value by applying some kind of resummations. The same result was also derived by using the renormalization group approach [6].…”

Section: Introductionmentioning

confidence: 99%

THE TYPE OF THE PHASE TRANSITION AND COUPLING VALUES IN λϕ⁴ MODEL

Bordag

Demchik

Gulov

et al. 2012

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

The temperature induced phase transition is investigated in the one-component scalar field φ 4 model on the lattice. Using the GPU cluster a huge amount of Monte Carlo simulation data is collected for a wide interval of coupling values. This gives a possibility to determine the low bound on the coupling constant λ 0 when the transition happens and investigate its type. We found that for the values of λ close to this bound a weak-first-order phase transition takes place. It converts into a second order one with the increase of λ. A comparison with the results obtained in analytic and numeric calculations by other authors is given.

show abstract

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

Cited by 40 publications

References 46 publications

Symmetry-improved CJT effective action

Symmetry-improved CJT effective action

Thermodynamics ofO(N)sigma models:1/Ncorrections

THE TYPE OF THE PHASE TRANSITION AND COUPLING VALUES IN λϕ⁴ MODEL

Contact Info

Product

Resources

About

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

Cited by 40 publications

References 46 publications

Symmetry-improved CJT effective action

Symmetry-improved CJT effective action

Thermodynamics ofO(N)sigma models:1/Ncorrections

THE TYPE OF THE PHASE TRANSITION AND COUPLING VALUES IN λϕ4 MODEL

Contact Info

Product

Resources

About

THE TYPE OF THE PHASE TRANSITION AND COUPLING VALUES IN λϕ⁴ MODEL