Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system

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 model 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. This talk is based on Ref. [1].

[1] T. Yokota, J. Haruyama, O. Sugino, Phys. Rev. E 104, 014124 (2021)