  Recently, Dvali, Gomez, and Mukhanov have investigated a classical lambda
phi^4 model with external source and without mass and they have clarified that
there are underlying renormalization group structure, including the phenomenon
of the dimensional transmutation, at purely classical level. Especially when
the coupling lambda is negative, the classical beta function shows the property
of asymptotic freedom as in QCD. In this paper, we investigate the lambda phi^4
model with mass, and clarify the role of the mass. The obtained classical beta
function is identical with that of the massless lambda phi^4 model up to the
corrections of the ratio of the IR cutoff to UV cutoff, and describes the
renormalization flow same as the massless theory. We also found that the
dynamically generated scale of massive theory is larger than that of massless
theory, which could be due to the screening effect of the mass term.
