Phase transition in scalar $φ^4$-theory beyond the super daisy resummations

Details Phase transition in scalar $φ^4$-theory beyond the super daisy resummations Phase transition in scalar $φ^4$-theory beyond the super daisy resummations

2000-06-13

arxiv.org/abs/hep-th/0006089v1

J.Phys.A34:461-472,2001

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1088/0305-4470/34/3/310

The temperature phase transition in scalar $\phi^4(x)$ field theory with spontaneous symmetry breaking is investigated in a partly resummed perturbative approach. The second Legendre transform is used and the resulting gap equation is considered in the extrema of the free energy functional. It is found that the phase transition is of first order in the super daisy as well as in a certain beyond super daisy resummations. No unwanted imaginary parts in the free energy are found but a loss of the smallness of the effective expansion parameter near the phase transition temperature is found in both cases. This means an insufficiency of the resummations or a deficit of the perturbative approach.

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