2009/09/29 by Thomas Jackson, T. S. Jackson, N. Read · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Biology #Combinatorics #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Spanning tree #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech #math.PR
paper · pdf · doi:10.1103/physreve.81.021131
published as Phys. Rev. E 81, 021131 (2010) · 33 pages, 5 figures, submitted to PRE; part I available at arXiv:0902.3651
arxiv created 2009/09/29 · openalex publication_date 2010/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Dp of paths on the latter MST; our previous results lead us to predict that Dp=2 for d>dc=6. Using a renormalization-group approach, we confirm the result for d>6 and calculate Dp to first order in \ensuremathε=6\ensuremath-d for d<6 using the connection with critical percolation, with the result Dp=2\ensuremath-\ensuremathε∕7+O(\ensuremathε2).