One-dimensional fluids with second nearest-neighbor interactions

TL;DR

This paper investigates approximate solutions for one-dimensional fluids with second nearest-neighbor interactions, extending beyond the exactly solvable first-nearest-neighbor models, and validates these approximations against Monte Carlo simulations.

Contribution

It introduces and compares various approximate methods for second nearest-neighbor interactions in 1D fluids, a problem lacking exact solutions.

Findings

Excellent agreement between approximations and Monte Carlo simulations.

Approximate solutions effectively model second nearest-neighbor fluids.

Methodology applicable to square-well and two-step potentials.

Abstract

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest-neighbor probability distribution function, $p_1(r)$, is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest-neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of $p_1(r)$ is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest-neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.