Critical Temperature for the $\LAMBDA (\PHI^{4})_{4}$ Theory within the $\DELTA$ -Expansion

We apply the $\delta$-expansion perturbation scheme to the $\lambda \phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\delta$-expansion the interaction term is written as $\lambda (\phi^{2})^{ 1 + \delta}$ and $\delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $\delta$. The results are compared with the usual loop-expansion at f...

The optimized linear $\delta$-expansion is applied to the $\lambda \phi^4$ theory at high temperature. Using the imaginary time formalism the thermal mass is evaluated perturbatively up to order $\delta^2$. A variational procedure associated with the method generates nonperturbative results which are used to obtain the critical temperature for the phase transition. Our results are compared with the ones given by propagator dressing methods.

We discuss the universal critical behavior of a selfinteracting scalar field theory at finite temperature as obtained from approximate solutions to nonperturbative renormalization group (RG) equations. We employ a formulation of the RG-equations in real-time formalism which is particularly well suited for a discussion of the thermal behavior of theories which are weakly coupled at T=0. We obtain the equation of state and critical exponents of the theory with a few percent acc...

At high temperatures a four dimensional field theory is reduced to a three dimensional field theory. In this letter we consider the $\phi^4$ theory whose parameters are chosen so that a thermal phase transition occurs at a high temperature. Using the known properties of the three dimensional theory, we derive a non-trivial correction to the critical temperature.

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 ...

A self-consistent renormalization scheme at finite temperature and zero momentum is used together with the finite temperature renormalization group to study the temperature dependence of the mass and the coupling to one-loop order in the $(\phi^3)_6$- and $(\phi^4)_4$-models. It is found that the critical temperature is shifted relative to the naive one-loop result and the coupling constants at the critical temperature get large corrections. In the high temperature limit of t...

The effective potential for the local composite operator $\phi^{2}(x)$ in $\lambda \phi^{4}$-theory is investigated at finite temperature in an approach based on path-integral linearisation of the $\phi^4 $-interaction. At zero temperature, the perturbative vacuum is unstable, because a non-trivial phase with a scalar condensate $\langle \phi ^{2} \rangle _{0}$ has lower effective action. Due to field renormalisation, $\langle \lambda \phi ^{2} \rangle _{0}$ is renormalisatio...

In this paper the phase structure of the massive $\lambda \phi^4$ model at finite temperature ($T \neq 0$) is investigated by applying a resummation method inspired by the renormalization-group (RG) improvement to the one-loop effective potential. The resummation method a la RG-improvement is shown to work quite succesfully by resumming up systematically large correction-terms of $O(\lambda T/\mu)$ and of $O(\lambda (T/\mu)^2)$. The temperature-dependent phase transition of t...

Effective critical exponents for the \lambda \phi^4 scalar field theory are calculated as a function of the renormalization group block size k_o^{-1} and inverse critical temperature \beta_c. Exact renormalization group equations are presented up to first order in the derivative expansion and numerical solutions are obtained with and without polynomial expansion of the blocked potential. For a finite temperature system in d dimensions, it is shown that \bar\beta_c = \beta_c k...

The thermodynamics of a scalar field with a quartic interaction is studied within the linear delta expansion (LDE) method. Using the imaginary-time formalism the free energy is evaluated up to second order in the LDE. The method generates nonperturbative results that are then used to obtain thermodynamic quantities like the pressure. The phase transition pattern of the model is fully studied, from the broken to the symmetry restored phase. The results are compared with those ...