Theory of minimum spanning trees. II. Exact graphical methods and perturbation expansion at the percolation threshold
- Department of Physics, Yale University, P.O. Box 208120, New Haven, Connecticut 06520-8120 (United States)
Continuing the program begun by the authors in a previous paper, we develop an exact low-density expansion for the random minimum spanning tree (MST) on a finite graph and use it to develop a continuum perturbation expansion for the MST on critical percolation clusters in space dimension d. The perturbation expansion is proved to be renormalizable in d=6 dimensions. We consider the fractal dimension D{sub p} of paths on the latter MST; our previous results lead us to predict that D{sub p}=2 for d>d{sub c}=6. Using a renormalization-group approach, we confirm the result for d>6 and calculate D{sub p} to first order in epsilon=6-d for d<6 using the connection with critical percolation, with the result D{sub p}=2-epsilon/7+O(epsilon{sup 2}).
- OSTI ID:
- 21344708
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 81, Issue 2; Other Information: DOI: 10.1103/PhysRevE.81.021131; (c) 2010 The American Physical Society; ISSN 1539-3755
- Country of Publication:
- United States
- Language:
- English
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