Magnetic analog of self-avoiding random walks (polymer chains) on a lattice
- 1 October 1981
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 24 (4), 2096-2108
- https://doi.org/10.1103/physreva.24.2096
Abstract
It is shown that if one considers the limit of a magnetic system consisting of -component classical spins on a lattice, one indeed obtains a correspondence with a system of self-avoiding random walks; that is, polymer chains with excluded volume in a solution, but the correspondence is not isomorphic. It turns out that and do not serve as the activities for the polymer system, which, in fact, are given by and , where . Moreover, the polymer free energy is also different from the magnetic free energy in the limit . Various polymer correlation functions are calculated and are found to be different from those proposed by other authors. It is also shown that satisfies the proper convexity properties, even though does not.
Keywords
This publication has 15 references indexed in Scilit:
- Self avoiding walk and supersymmetryJournal de Physique Lettres, 1980
- Finite cluster partition functions for the D-vector modelJournal of Physics A: General Physics, 1976
- Renormalization group calculation of polymer properties in dilute solutionJournal of Physics A: General Physics, 1976
- Self-interacting walks, random spin systems, and the zero-component limitPhysical Review B, 1976
- Solutions of Flexible Polymers. Neutron Experiments and InterpretationMacromolecules, 1975
- Critical properties of many-component systemsPhysical Review B, 1975
- Lagrangian theory for a self-avoiding random chainPhysical Review A, 1974
- An exact relation between the classical n-vector model ferromagnet and the self-avoiding walk problemJournal of Physics C: Solid State Physics, 1973
- Exponents for the excluded volume problem as derived by the Wilson methodPhysics Letters A, 1972
- Functional Integrals and Polymer StatisticsAdvances in Chemical Physics, 1972