### Abstract

Positional ordering of a two-dimensional fluid of hard disks is examined in tubes so narrow that only nearest neighbor interactions take place. Using the exact transfer-matrix method the transverse and longitudinal pressure components and the correlation function are determined numerically. Fluid-solid phase transition does not occur even in the widest tube, where the method just loses its exactness, but the appearance of a dramatic change in the equation of state and the longitudinal correlation function shows that the system undergoes a structural change from a fluid to a solid-like order. The pressure components show that the collisions are dominantly longitudinal at low densities, while they are transverse in the vicinity of the close packing density. The transverse correlation function shows that the size of solid-like domains grows exponentially with increasing pressure and the correlation length diverges at close packing. It is possible to find an analytically solvable model by expanding the contact distance up to first order. The approximate model, which corresponds to a system of hard parallel rhombuses, behaves very similarly to the system of hard disks.

Original language | English |
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Article number | P11006 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2011 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 1 2011 |

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### Keywords

- classical Monte Carlo simulations
- correlation functions
- fluids in confined geometries
- interfacial phenomena and wetting
- rigorous results in statistical mechanics

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2011*(11), [P11006]. https://doi.org/10.1088/1742-5468/2011/11/P11006