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

We calculate the self-energy at finite temperature in scalar $\lambda\phi ^4$ theory to second order in a modified perturbation expansion. Using the renormalisation group equation to tame the logarithms in momentum, it gives an equation to determine the critical temperature. Due to the infrared freedom of the theory, this equation is satisfied, irrespective of the value of the temperature. We conclude that there is no second order phase transition in this theory.

The linear $\delta$ expansion is used to obtain corrections up to O$(\delta^2)$ to the self-energy for a complex scalar field theory with a $\lambda (\phi^{\star}\phi)^2$ interaction at high temperature and non-zero charge density. The calculation is done in the imaginary-time formalism via the Hamiltonian form of the path integral. Nonperturbative results are generated by a systematic order by order variational procedure and the dependence of the critical temperature on the ...

Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda phi^4 theory are performed in d=4 Euclidean space for both low and high temperature limits. We generate a set of coupled equations for the mass parameter and the coupling constant from the renormalization group flow equation. Dimensional reduct...

In this paper a resummation method inspired by the renormalization-group improvement is applied to the one-loop effective potential (EP) in massive scalar $\phi^4$ model at $T\neq0$. By investigating the phase structure of the model at $T \neq 0$ we get the following observations; i) Starting from the perturbative calculations with the theory renormalized at an arbitrary mass-scale $\mu$ and at an arbitrary temperature $T_0$, we can in principle fully resum terms of $O(\lambd...

We suggest that the $\phi^4$ model is only a polynomial approximation to a more fundamental theory. As a consequence the high temperature regime might not be correctly described by this model. If this turns out to be true then several results concerning e.g., critical temperatures, symmetry restoration at high temperature and high temperature expansions should be reconsidered. We illustrate our conjecture by using the Nambu-Goto string model. We compare a two-loop calculation...

I present a sequence of non-perturbative approximate solutions for scalar $\phi^4$ theory for arbitrary interaction strength, which contains, but allows to systematically improve on, the familiar mean-field approximation. This sequence of approximate solutions is apparently well-behaved and numerically simple to calculate since it only requires the evaluation of (nested) one-loop integrals. To test this resummation scheme, the case of $\phi^4$ theory in 1+1 dimensions is cons...

By the concurrent use of two different resummation methods, the composite operator formalism and the Dyson-Schwinger equation, we re-examinate the behavior at finite temperature of the O(N)-symmetric $\lambda\phi^{4}$ model in a generic D-dimensional Euclidean space. In the cases D=3 and D=4, an analysis of the thermal behavior of the renormalized squared mass and coupling constant are done for all temperatures. It results that the thermal renormalized squared mass is positiv...

We study the optimized perturbation theory (OPT) at finite temperature, which is a self-consistent resummation method. Firstly, we generalize the idea of the OPT to optimize the coupling constant in lambda phi^4 theory, and give a proof of the renormalizability of this generalized OPT. Secondly, the principle of minimal sensitivity and the criterion of the fastest apparent convergence, which are conditions to determine the optimal parameter values, are examined in lambda phi^...

The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even in the simplest case of $1+1$ dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong coupling parameters to each other. He used a clevert variational technique ( back to kleinert and Feynman) to extract accurate values for the strong coupling parameters from which he was able to extract precise critical exponents. In this w...

We have applied the recently proposed renormalization group improvement procedure of the finite temperature effective potential, and have investigated extensively the phase structure of the massive scalar $\phi^4$ model, showing that the $\phi^4$ model has a rich 3-phase structure at $T \neq 0$, two of them are not seen in the ordinary perturbative analysis. Temperature dependent phase transition in this model is shown to be strongly the first order.