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Accurate and efficient ways to analyze classical liquids are desired in various contexts including chemical reactions. Traditional approaches include the renormalization-group (RG) methods such as the hierarchical reference theory. However, these traditional approaches rely on the knowledge of hard-core reference systems to include the effect of short-range repulsion. Recently, we have developed an RG approach that does not rely on a hard-core reference system [1]. We have introduced the functional RG to rigorously describe the RG flow and the cavity distribution functions to treat short-range repulsion. In this talk, I will present the formulation and numerical demonstrations in a one-dimensional solvable model, where our approach shows better accuracy than the conventional integral-equation methods such as the hypernetted chain and the Percus-Yevick equation.

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

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