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How the overlap of excluded volume determines the configurational energy landscape and “thermodynamics” in the “one to five hard disks in a box” system

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  • Huerta, Adrián
  • Toledo-Marín, J. Quetzalcóatl
  • Naumis, Gerardo G.

Abstract

In this work, the effects of excluded volume are studied in the “one to five hard disks in a box” system, based in writing an exact equation of state in which the excluded volume overlap is related with the spare volume. For one and two disks in different types of cages, the attractive and repulsive forces are calculated analytically. These attractive forces are due to excluded volume overlap allowing second neighbors to have an effective interaction, a fact that is usually neglected when considering only collisions with first-neighbors. The same effects are observed for numerical computations with five-disks in a box, as the distributions of distances between disks and disks to walls suggest. Also, numerically exact equations of state are presented for the one to five hard disks in a box system from a direct-sampling Monte Carlo procedure. All these results indicate that first and second-neighbor excluded volume interactions are essential to determine the energy landscape topology. This work supports previous observations which suggests that second-neighbor excluded volume interactions in hard-core systems are related with phase transitions.

Suggested Citation

  • Huerta, Adrián & Toledo-Marín, J. Quetzalcóatl & Naumis, Gerardo G., 2020. "How the overlap of excluded volume determines the configurational energy landscape and “thermodynamics” in the “one to five hard disks in a box” system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
  • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320448
    DOI: 10.1016/j.physa.2019.123666
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    References listed on IDEAS

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    1. Yufeng Wang & Yu Wang & Dana R. Breed & Vinothan N. Manoharan & Lang Feng & Andrew D. Hollingsworth & Marcus Weck & David J. Pine, 2012. "Colloids with valence and specific directional bonding," Nature, Nature, vol. 491(7422), pages 51-55, November.
    2. Bowles, Richard K. & Speedy, Robin J., 1999. "Five discs in a box," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(1), pages 76-87.
    3. Speedy, Robin J., 1994. "Two disks in a box," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 210(3), pages 341-351.
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    1. Hoover, W.G., 1995. "Comment on “Two disks in a box” [R.J. Speedy, Physica A 210 (1994) 341]," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(1), pages 195-195.

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