The thermal coupling constant and the gap equation in the λϕD4 model

Abstract By the concurrent use of two different resummation methods, the composite operator formalism and the Dyson-Schwinger equation, we re-examine the behavior at finite temperature of the O(N)-symmetricλϕ4 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 carried out for all temperatures. It results that the thermal renormalized squared mass is positive and increases monotonically with the temperature. The behavior of the thermal coupling constant is quite different in odd- or even-dimensional space. In D = 3, the thermal coupling constant decreases up to a minimum value different from zero and then grows monotonically as the temperature increases. In the case D = 4, it is found that the thermal renormalized coupling constant tends, in the high-temperature limit, to a constant asymptotic value. Also for general D-dimensional Euclidean space, we are able to obtain a formula for the critical temperature of the second-order phase transition. This formula agrees with previous known values at D = 3 and D = 4.