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.
KeywordsPartition Function Ising Model Large Eigenvalue Pair Correlation Function Pair Distribution Function
Unable to display preview. Download preview PDF.
- 2.J. A. Schellman, Compt. Rend. Tray. Lab. Carlsberg. Ser. Chim 29, 230 (1955).Google Scholar
- E. L. Lieb and D. C. Mattis, Mathematical Physics in One Dimension ( Academic Press, New York, 1966 ).Google Scholar
- T. M. Birshtein and O. B. Ptitsyn, Conformations of Macromolecules ( Interscience Publishers, New York, 1966 ).Google Scholar
- P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience Publishers, New York, 1969). More specific applications to biopolymers:Google Scholar
- D. Poland and A. Scheraga, Theory of Helix-Coil Transitions in Biopolymers ( Academic Press, New York, 1970 ).Google Scholar