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Square lattice calculations for the general dimer and trimer problems using the Kikuchi method

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  • Kaye, R.D.
  • Burley, D.M.

Abstract

Square lattice models for the general dimer and trimer problems are considered. A secondary lattice for the dimer problem is constructed, and a double square Kikuchi calculation produces an athermal molecular freedom within 2% of the known exact result. With interactions, departures from ideality of mixing entropy and vapour pressure are calculated at different temperatures, and an asymmetrical phase separation occurs at a reduced temperature 0.08. The general trimer problem is considered in a single square Kikuchi calculation. A single interaction is included. The molecular freedom and thermodynamic non-ideality of rigid linear, rigid angled and flexible trimers are compared. In the rigid linear case a phase separation occurs at reduced temperature 0.04. The molecular freedom of rigid linear trimers is calculated using higher Kikuchi approximations, and the result agrees well with previous estimates.

Suggested Citation

  • Kaye, R.D. & Burley, D.M., 1977. "Square lattice calculations for the general dimer and trimer problems using the Kikuchi method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(3), pages 499-514.
    • Handle: RePEc:eee:phsmap:v:87:y:1977:i:3:p:499-514
    DOI: 10.1016/0378-4371(77)90047-4
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    References listed on IDEAS

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    1. Alemson, M A & Burley, H T, 1974. "Demand and Entry into an Oligopolistic Market: A Case Study," Journal of Industrial Economics, Wiley Blackwell, vol. 23(2), pages 109-124, December.
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    Cited by:

    1. Kaye, R.D., 1981. "Orientational transitions in a dimer system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 105(1), pages 347-356.

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