  The renormalization-group approaches for classical liquids in previous works
require a repulsive reference such as a hard-core one when applied to systems
with short-range repulsion. The need for the reference is circumvented here by
using a functional renormalization group approach for integrating the
hierarchical flow of correlation functions along a path of variable interatomic
coupling. We introduce the cavity distribution functions to avoid the
appearance of divergent terms and choose a path to reduce the error caused by
the decomposition of higher order correlation functions. We demonstrate using
an exactly solvable one-dimensional models that the resulting scheme yields
accurate thermodynamic properties and interatomic distribution at various
densities when compared to integral-equation methods such as the hypernetted
chain and the Percus-Yevick equation, even in the case where our hierarchical
equations are truncated with the Kirkwood superposition approximation, which is
valid for low-density cases.

Statistical Mechanics;Soft Condensed Matter;High Energy Physics - Theory;Nuclear Theory