Role of the equilibrium size of Kadanoff blocks in the loop-expansion technique

A method developed by the present authors in a previous paper [Phys. Rev. E 57, 2594 (1998)] leads to the introduction of the equilibrium size of the Kadanoff blocks as a useful tool to approach the critical properties of the phi^4 model. The present paper aims to elucidate the role of the equilibrium size of the Kadanoff blocks in the loop-expansion technique currently used in the field-theoretic renormalization. While the standard results are readily obtained, aspects emerge that help clarify the true nature of the smallness parameter in the loop-expansion technique.