Scalar O(n) Model at Finite Temperature— 2pi Effective Potential in Different Approximations

Abstract

We calculate the two-particle irreducible (2PI) effective potential of the O(N ) linear sigma model in 1+1 dimensions. The approximations we use are the nextto-leading order of a 1/N expansion (for arbitrary N ) and a kind of "resummed loop approximation" for N = 1. We show that the effective potential of the 1/N expansion is convex for N = 4 and N = 10 whereas it is not for the "loop" expansion and the case N = 1 of the 1/N expansion.

Two-particle irreducible finite temperature effective potential of theO(N)linear sigma model in1+1dimensions at next-to-leading order ofBaacke1, Michalski2 2004Phys. Rev. DSelf Cite

“…In contrast to that, the 2PPI approximation in equilibrium displays spontaneous symmetry breaking, and so does the 2PI approximation both with correct N = 1 combinatorics and with 1/N combinatorics [38]. This is due to the fact that these calculations do not encompass kink transitions which are of order 1/λ.…”

“…Coming back to the simulations in 1 + 1 dimensions for the case N = 1 [28,30] spontaneous symmetry breaking was found in the late time behavior of the Hartree approximation, whereas in both the 2PI and the 2PPI the mean field approaches the symmetric phase at late times. In contrast to that, the 2PPI approximation in equilibrium displays spontaneous symmetry breaking, and so does the 2PI approximation both with correct N = 1 combinatorics and with 1/N combinatorics [38]. This is due to the fact that these calculations do not encompass kink transitions which are of order 1/λ.…”

One-meson-loop NJL model: Effect of collective and noncollective excitations on the quark condensate at finite temperature

“…Including fluctuations in the NJL model, however, is not an easy task [23]. For some works, including beyond MF corrections to the NJL model and linear sigma model see [24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Nonequilibrium evolution ofΦ4theory in1+1dimensions in the two-particle point-irreducible formalism

“…Recent progress in the 2PPI formalism includes the demonstration or renormalizability [17,18] and some finite-temperature two-loop calculations in 3 + 1 dimensions. An interesting result was that for N = 1 [19] and for N = 1 [20] the order of the phase transition between the spontaneously broken and symmetric phases becomes second order in the 2-loop approximation, while it is first order in the Hartree approximation. The results for the 2PPI expansion have been compared to exact results in [21] for the anharmonic oszillator; even more recently [22] the two-loop approximation has been compared, in 1 + 1 dimensions, with exact results of the Gross-Neveu model.…”