Beware of density dependent pair potentials

TL;DR

Density-dependent pair potentials are useful but complex tools in condensed matter physics, requiring careful consideration of their derivation and application to avoid inconsistencies in thermodynamic property calculations.

Contribution

This paper highlights the subtle issues and potential pitfalls in using density-dependent pair potentials, emphasizing the importance of the derivation route and coarse-graining procedures.

Findings

Incorrect use can lead to ensemble-dependent thermodynamic properties

Effective potentials may not reproduce all physical properties accurately

Illustrated with examples including liquid Argon and charged systems

Abstract

Density (or state) dependent pair potentials arise naturally from coarse-graining procedures in many areas of condensed matter science. However, correctly using them to calculate physical properties of interest is subtle and cannot be uncoupled from the route by which they were derived. Furthermore, there is usually no unique way to coarse-grain to an effective pair potential. Even for simple systems like liquid Argon, the pair potential that correctly reproduces the pair structure will not generate the right virial pressure. Ignoring these issues in naive applications of density dependent pair potentials can lead to an apparent dependence of thermodynamic properties on the ensemble within which they are calculated, as well as other inconsistencies. These concepts are illustrated by several pedagogical examples, including: effective pair potentials for systems with many-body interactions, and the mapping of charged (Debye-H\"{u}ckel) and uncharged (Asakura-Oosawa) two-component systems onto effective one-component ones.