Thermal effective potential of the O(N) linear σ model

Abstract

The finite-temperature effective potential of the O(N) linear σ model is studied, with emphasis on the implications for the investigation of hot hadron dynamics. The contributions from all the "bubble diagrams" are fully taken into account for arbitrary N; this also allows to address some long-standing issues concerning the use of non-perturbative approaches in (finite-temperature) field theory.

Study of the O(N) linear $\sigma$ model at finite temperature using the 2PPI expansion

“…This model has always been a fertile ground to test ideas and check approximations in finite temperature quantum field theory [3] and has recently attracted renewed interest [4][5][6][7][8][9][10][11] because of its relevance to the thermodynamics of chiral symmetry in Q.C.D. Many treatments of finite T O(N) linear σ-model use the Hartree approximation which sums bubble graphs (daisy and superdaisy graphs).…”

“…This sums self energy insertions but comes at the cost of introducing a self consistency condition which in general entails intractable non-local integral equations. When restricted to order λ, the 2PI expansion sums daisy and superdaisy graphs which alleviates some of the problems at finite T [4]. However, it is not feasible to extend this approach to higher order in λ and therefore some of the basic problems of the O(N) linear σ-model at finite T are still unsolved.…”

On the symmetry improved CJT formalism in the O(4) linear sigma model

“…5 MeV. In order to analyze the order of phase transition, in the spontaneous symmetry breaking phase, that is φ = 0, from the gap equations (33) and the relationship in Eqs.…”

“…As a quite popular model, the linear sigma model [3] for the phenomenology of QCD has been composed to describe the vacuum structure with incorporating chiral symmetry and its spontaneous breaking. The model can be used to describe a restoration of the chiral symmetry at finite temperature in the Hartree-Fock or Hartree approximation [1,[4][5][6][7][8][9][10][11][12] within the Cornwall-Jackiw-Tomboulis (CJT) formalism [13], also at finite isospin chemical potential [14][15][16][17][18]. However, except the case in the larger-N approximation [5][6] [7], these kinds of studies suffer from two major drawbacks.…”

Bose–Einstein condensation and chiral phase transition in linear sigma model

“…There are some discussions concerning the renormalization on the CJT formalism in different models [16,18,19]. Recent investigation about the renormalization of the O(N) linear sigma model has been addressed in [11].…”