Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2011/11/P11006
Keywords
correlation functions; rigorous results in statistical mechanics; classical Monte Carlo simulations; fluids in confined geometries; interfacial phenomena and wetting
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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.
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