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Statistical mechanics of quasi-one-dimensional systems

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  • Moraal, H.

Abstract

A definition of a quasi-one-dimensional system as a generalized Cayley or Husimi tree with a nonzero surface to bulk ratio in the thermodynamic limit is given. Sufficient conditions for the existence of the thermodynamic limit of the free energy for such a system are derived and a thorough discussion of the thermodynamic limit properties of the one-particle distribution functions is given. These results are made more precise for the case of systems with Hamiltonians which are invariant under a special type of measure-preserving group of transformations, in particular for the d-dimensional rotation group. For this latter case, the phase transitions which can occur in quasi-one-dimensional systems upon application of small external fields are studied in some detail. A number of completely solved examples is given to illustrate the general theory. These include the classical Heisenberg model on a Cayley tree and generalizations thereof.

Suggested Citation

  • Moraal, H., 1976. "Statistical mechanics of quasi-one-dimensional systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(3), pages 457-484.
    • Handle: RePEc:eee:phsmap:v:85:y:1976:i:3:p:457-484
    DOI: 10.1016/0378-4371(76)90020-0
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    1. Arnold Schwarz, 1958. "Neuere Auffassungen über die Umschichtung der Berufe," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 94(I), pages 68-75, March.
    2. Snider, Thomas E., 1972. "Branch Banking And Loan Portfolio Changes- The Virginia Experience," 1972 Annual Meeting, August 20-23, Gainesville, Florida 284611, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
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