The study of one-dimensional (1-D) systems is of interest for two main reasons. First, there are actual systems that are linear, such as linear polymers, proteins, and nucleic acids. Although all of these occupy three-dimensional space, their main properties are determined by the 1-D sequence of units and bonds. Second, these models are usually easily solvable. Therefore some general properties, theorems, conjectures, approximations, and the like may be tested on a 1-D system. The answers we obtain are sometimes also relevant to three-dimensional systems. Finally, the methods used to solve the 1-D partition functions are elegant and in themselves aesthetically satisfying.


Partition Function Ising Model Large Eigenvalue Pair Correlation Function Pair Distribution Function 
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  1. 1.
    T. L. Hill, Proc. Natl. Acad. Sci. U.S.A 57, 227 (1967).PubMedCentralCrossRefPubMedGoogle Scholar
  2. 2.
    J. A. Schellman, Compt. Rend. Tray. Lab. Carlsberg. Ser. Chim 29, 230 (1955).Google Scholar
  3. 3.
    S. Lifson and A. Roig, J. Chem. Phys 34, 1963 (1961).CrossRefGoogle Scholar

Suggested Readings

  1. E. L. Lieb and D. C. Mattis, Mathematical Physics in One Dimension ( Academic Press, New York, 1966 ).Google Scholar
  2. T. M. Birshtein and O. B. Ptitsyn, Conformations of Macromolecules ( Interscience Publishers, New York, 1966 ).Google Scholar
  3. P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience Publishers, New York, 1969). More specific applications to biopolymers:Google Scholar
  4. D. Poland and A. Scheraga, Theory of Helix-Coil Transitions in Biopolymers ( Academic Press, New York, 1970 ).Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Arieh Ben-Naim
    • 1
  1. 1.Department of Physical ChemistryThe Hebrew University of JerusalemJerusalemIsrael

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