Computation of the RG Improved Effective Potential: Details of the Numerical Analysis

著者

Hisao NAKKAGAWA
(Hisao nakagawa)

教養部

Hiroshi YOKOTA
(Hisao yokota)

教養部

版

publisher

出版地

奈良

出版者

奈良大学

上位タイトル

奈良大学紀要
(Memoirs of the Nara University).
Vol.26号,
(1998.
03)
,p.1-
9

識別番号

ISSN

03892204

抄録

Recently we have applied the newly proposed renormalization group (RG) improvement procedure of the finite temperature effective potential to the massive φ4 model, and have shown that i) the massive scalar φ4 model has a rich three-phase structure at T≠0, two of them are not seen in the ordinary perturbative analysis, and that ii) the 0(N) symmetric massive φ4 model has a two-phase structure, one of them are not seen in the perturbative analysis. Both results indicate that the new RG improvement procedure is really an efficient procedure that can incorpolate
the nonperturbative effect by resumming correctly the dominant large erturbative
corrections through the RG technique. To reach the above observations,however,
a bit tedious numerical analysis is unevitable, which is the cost to be paid. In thispaper we present the details of the numerical analysis; where the trouble in numerical computation may arise, how it can be resolved, and what is the reliability of the numerical computation. The last problem, i.e., reliability of the computation is studied by comparing the results of numerical computation with that of the high temperature expansion of the full formula. We find that the method we have made use of in the numerical computation is quite successful, giving even in the most troublesome cases the three significant figures agreement with the high temperature expansion. Results on the phase structure of the 0(N) symmetric massive φ4 model obtained by the numerical analysis are briefly given.