Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution

Abstract

The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the triangle-well and the ramp potentials is worked out. In contrast to previous studies, where the radial distribution function $g(r)$ was obtained numerically from the structure factor by Fourier inversion, we provide a fully analytic representation of $g(r)$ up to any desired distance. The solution is employed to perform an extensive study of the equation of state, the excess internal energy per particle, the residual multiparticle entropy, the structure factor, the radial distribution function, and the direct correlation function. In addition, scatter plots of the bridge function versus the indirect correlation function are used to gauge the reliability of the hypernetted-chain, Percus--Yevick, and Martynov--Sarkisov closures. Finally, the Fisher--Widom and Widom lines are obtained in the case of the triangle-well model.

arXiv comment19 pages, 9 figures

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• Exploring anisotropic pressure and spatial correlations in strongly confined hard-disk fluids. Exact results
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• Universality of the close packing properties and markers of isotropic-to-tetratic crossover in quasi-one-dimensional superdisk fluid
• On a conjecture concerning the Fisher--Widom line and the line of vanishing excess isothermal compressibility in simple fluids
• Exact anisotropic properties of hard spheres in narrow cylindrical confinement
• Ordering and association of patchy particles in quasi-one-dimensional channel
• Discontinuous Structural Transitions in Fluids with Competing Interactions
• Finite-size effects and thermodynamic limit in one-dimensional Janus fluids
• 1D fluids with repulsive nearest-neighbour interactions: Low-temperature anomalies