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Repulsive particles on a two-dimensional lattice

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  • Watson, G.I.

Abstract

The problem of finding the minimum-energy configurations of particles on a square lattice, subject to short-ranged repulsive interactions, is studied analytically. The study is relevant to charge-ordered states of interacting fermions, as described by the spinless Falicov-Kimball model. A simple model is introduced, corresponding to the limit of a two-body potential which is a very rapidly decreasing convex function of distance. Its ground states are found rigorously for certain density ranges, including half filling. These agree with known properties of neutral ground states of the large-U Falicov-Kimball model, suggesting a characterization of the latter as “most homogeneous” configurations. For lower densities, a family of ground states is found having the novel property that they are aperiodic even when the particle density is a rational number. In some cases, local phase separation suggests an inherent sensitivity to the detailed form of the interaction potential.

Suggested Citation

  • Watson, G.I., 1997. "Repulsive particles on a two-dimensional lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(1), pages 253-274.
    • Handle: RePEc:eee:phsmap:v:246:y:1997:i:1:p:253-274
    DOI: 10.1016/S0378-4371(97)00349-X
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    References listed on IDEAS

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    1. Macris, N., 1996. "Periodic ground states in simple models of itinerant fermions interacting with classical fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(3), pages 648-656.
    2. Kimball, Warren F., 1969. "“Beggar My Neighbor†: America and the British Interim Finance Crisis, 1940–1941," The Journal of Economic History, Cambridge University Press, vol. 29(4), pages 758-772, December.
    3. Shane, Scott & Kolvereid, Lars & Westhead, Paul, 1991. "An exploratory examination of the reasons leading to new firm formation across country and gender," Journal of Business Venturing, Elsevier, vol. 6(6), pages 431-446, November.
    4. Miracle-Solé, S., 1996. "A study of the large coupling expansion in the Falicov-Kimball model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(3), pages 686-701.
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    Cited by:

    1. Derzhko, Volodymyr & Jȩdrzejewski, Janusz, 2003. "From phase separation to long-range order in a system of interacting electrons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(3), pages 449-465.

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