Polymerization on the Diamond Hierarchical Lattice: The Migdal-Kadanoff Renormalization-Group Scheme
Document Type
Article
Publication Date
4-1-1990
Publication Title
Physical Review A
Abstract
The thermodynamics of the equilibrium polymerization model (grand-canonical ensemble of self-avoiding walks) in two dimensions is worked out by means of the Migdal-Kadanoff renormalization-group technique. This method involves renormalization-group flows in an eight-dimensional parameter space. At the critical point the number of relevant fields (positive exponents) is four. The leading exponent value differs by less than 1% from the (presumed) exact value. The results are exact for the polymerization problem defined on the diamond hierarchical lattice. Some results are peculiar to this lattice and are not expected to hold for Bravais lattices. For instance, the polymerized phase (infinite polymerization index) is dilute (zero density of chemical bonds).
Repository Citation
Kaufman, Miron and Touma, J. E., "Polymerization on the Diamond Hierarchical Lattice: The Migdal-Kadanoff Renormalization-Group Scheme" (1990). Physics Faculty Publications. 2.
https://engagedscholarship.csuohio.edu/sciphysics_facpub/2
Original Citation
Kaufman, Miron and J. E. Touma. "Polymerization on the Diamond Hierarchical Lattice: The Migdal-Kadanoff Renormalization-Group Scheme." Physical Review A 41 (1990): 4371-4378.
DOI
10.1103/PhysRevA.41.4371
Version
Publisher's PDF
Publisher's Statement
Copyright 1990 American Physical Society. Available on publisher's site at http://pra.aps.org/abstract/PRA/v41/i8/p4371_1.
Volume
41
Issue
8
