Journal of Statistical Physics

, Volume 175, Issue 2, pp 269–288 | Cite as

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

  • Ana M. Montero
  • Andrés SantosEmail author


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.


One-dimensional fluids Nearest neighbors Triangle-well model Ramp model Radial distribution function Fisher–Widom line Widom line 



A.M.M. is grateful to the Ministerio de Educación, Cultura y Deporte (Spain) for a Beca-Colaboración during the academic year 2016–2017, which gave rise to this work. The research of A.S. has been supported by the Spanish Agencia Estatal de Investigación through Grant No. FIS2016-76359-P and the Junta de Extremadura (Spain) through Grant No. GR18079, both partially financed by Fondo Europeo de Desarrollo Regional funds.


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Authors and Affiliations

  1. 1.Aachen Institute for Advanced Study in Computational Engineering ScienceRWTH Aachen UniversityAachenGermany
  2. 2.Departamento de FísicaUniversidad de ExtremaduraBadajozSpain
  3. 3.Instituto de Computación Científica Avanzada (ICCAEx)Universidad de ExtremaduraBadajozSpain

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