Phase Structure of the Massive Scalar phi^4 Model at Finite Temperature -- Resummation Procedure a la RG improvement --

Abstract

In this paper a resummation method inspired by the renormalization-group improvement is applied to the one-loop effective potential (EP) in massive scalar $ϕ^4$ 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 $μ$ and at an arbitrary temperature $T_0$, we can in principle fully resum terms of $O(λT/μ)$ together with terms of $O(λ(T/μ)^2)$. The key idea is to fix the arbitrary RS-parameters so as to make both of one-loop radiative corrections to the mass as well as to the coupling vanish, ensuring the function form of the EP to be determined up to the next-to-leading order of large correction terms, thus absorbing completely those terms of $O(λ(T/μ)^2)$ and of $O(λT/μ)$. ii) If we start from the theory renormalized at the temperature of the environment $T$, the $O(λ(T/μ)^2)$-term resummation can be simply completed through the $T$-renormalization itself. With the lack of freedom we can set only one RS-fixing condition to absorb the large terms of $O(λT/μ)$, thus only the partial resummation of these terms can be carried out. iii) In the above two analyses the temperature-dependent phase transition of the model is shown with the analytic evaluation to proceed through the second order transition. The critical exponents are estimated analytically and are compared with those in other analyses. iv) Our resummation method does not work if we start from the theory renormalized at T=0.