The thermal coupling constant and the gap equation in the lambda phi(4)(D)model

By the concurrent use of two different resummation methods, the composite o perator formalism and the Dyson-Schwinger equation, we re-examine the behav ior at finite temperature of the O(N)-symmetric lambda phi(4) model in a ge neric D-dimensional Euclidean space. In the cases D = 3 and D = 4, an analy sis of the thermal behavior of the renormalized squared mass and coupling c onstant are carried out for all temperatures. It results that the thermal r enormalized squared mass is positive and increases monotonically with the t emperature. The behavior of the thermal coupling constant is quite differen t in odd- or even-dimensional space, In D = 3, the thermal coupling constan t decreases up to a minimum value different from zero and then grows monoto nically as the temperature increases. In the case D = 4, it is found that t he thermal renormalized coupling constant tends, in the high-temperature li mit, to a constant asymptotic value. Also for general D-dimensional Euclide an space, we are able to obtain a formula for the critical temperature of t he second-order phase transition. This formula agrees with previous known v alues at D = 3 and D = 4. (C) 1999 Elsevier Science B.V.