Abstract
We summarize results of the finite-temperature renormalization group approach, formalized by Matsumoto, Nakano and Umezawa in 1984, for the λ(ϕ4)4-model. The flow parameter is the reference temperature at which the mass parameter and the coupling constant of the theory are defined through renormalization conditions. We derive flow equations to one-loop order, and integrate numerically from zero temperature to above the critical temperature. The mass and the coupling constant both vanish at the critical temperature, and are positive below and above the critical region. In the critical region dimensional reduction to an effective 3D theory takes place. The leading behavior of the mass at high temperature is linear with a small logarithmic sub-leading contribution.
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