n-vector model in the limitn→0and the statistics of linear polymer systems: A Ginzburg-Landau theory

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Abstract
The statistics of linear polymer systems is investigated using the correspondence between self-avoiding random walks and the partition function for the n-vector magnetic model in the limit n→0. The magnetic problem is treated in the Ginzburg-Landau version. In this way we are able to perform the calculations for systems of finite size and thereby execute the n→0 limit in the proper way. A further advantage of our calculational approach is that it allows us to investigate the effects of restricted geometries. We demonstrate how to extract results for the one polymer system and explore its thermodynamic behavior in the mean-field and spin-wave approximation above and below the phase transition. Correspondence between Flory’s classical approach to understanding polymers and the magnetic analogy is derived and a calculational procedure for improvement and new insights are developed.