FINITE-TEMPERATURE RENORMALIZATION OF THE (PHI(4))(4)-MODEL

We summarize results of the finite-temperature renormalization group a pproach, formalized by Matsumoto, Nakano and Umezawa in 1984, for the lambda(phi(4))(4)-model. The flow parameter is the reference temperatu re at which the mass parameter and the coupling constant of the theory are defined through renormalization conditions. We derive flow equati ons to one-loop order, and integrate numerically from zero temperature to above tile critical temperature. The mass and the coupling constan t both vanish at the critical temperature, and are positive below and above the critical region. In the critical region dimensional reductio n to an effective 3D theory takes place. The leading behavior of the m ass at high temperature is linear with a small logarithmic sub-leading contribution.