  We investigate the critical behavior of the lambda phi^4 theory defined on
S^1 x R^d having two finite length scales beta, the circumference of S^1, and
k^{-1}, the blocking scale introduced by the renormalization group
transformation. By numerically solving the coupled differential RG equations
for the finite-temperature blocked potential U_{beta,k}(Phi) and the
wavefunction renormalization constant Z_{beta,k}(Phi), we demonstrate how the
finite-size scaling variable betabar = beta k determines whether the phase
transition is (d+1)- or d-dimensional in the limits betabar >> 1 and betabar <<
1, respectively. For the intermediate values of betabar, finite-size effects
play an important role. We also discuss the failure of the polynomial expansion
of the effective potential near criticality.
