Statistical mechanics of quasi-one-dimensional systems

H. Moraal

Physica A: Statistical Mechanics and its Applications, 1976, vol. 85, issue 3, 457-484

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.

Date: 1976
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:85:y:1976:i:3:p:457-484

DOI: 10.1016/0378-4371(76)90020-0

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