Non-perturbative approach to the effective potential of the $\lambda\phi^{4} theory at finite temperature

Joe Sato (University of Tokyo); Kenzo Ogure (Institute for Cosmic Ray Research); Tomohiro Inagaki (Kobe University)

Non-perturbative approach to the effective potential of the $\lambda\phi^{4} theory at finite temperature

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arxiv hep-th/9705133 v3 pith:K5AF3YKM submitted 1997-05-19 hep-th hep-ph

Tomohiro Inagaki (Kobe University) , Kenzo Ogure (Institute for Cosmic Ray Research) , Joe Sato (University of Tokyo) This is my paper · ORCID

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keywords effectivepotentialapproximationdifferentialequationfinitemethodnon-perturbative

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We construct a non-perturbative method to investigate the phase structure of the scalar theory at finite temperature. The derivative of the effective potential with respect to the mass square is expressed in terms of the full propagator. Under a certain approximation this expression reduces to the partial differential equation for the effective potential. We numerically solve the partial differential equation and obtain the effective potential non-perturbatively. It is found that the phase transition is of the second order. The critical exponents calculated in this method are consistent with the results obtained in Landau approximation.

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Spontaneous symmetry breaking induced by curvature : Analysis via non-perturbative 2PI Hartree approximation
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Curvature, via resummed 2PI Hartree self-energy, can induce spontaneous symmetry breaking for a minimally coupled scalar with positive mass squared in de Sitter spacetime.

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