Percolation on a Fractal With the Statistics of Planar Feynman Graphs: Exact Solution
Jul, 198813 pages
Published in:
- Mod.Phys.Lett.A 4 (1989) 1691
Report number:
- NBI-HE-88-44
View in:
Citations per year
Abstract: (WSP)
A new bond-percolation problem on a graph (fractal) randomly chosen from all planar Feynman graphs of zero-dimensional φ3 (or φ4) theory in the thermodynamical limit (infinite order of graphs) is solved exactly. At the percolation transition point pc the mean number of clusters per volume unit has the singularity (pc−p)4log (pc−p) which corresponds to the critical exponent α=−2. This model is a particular example of Potts models on dynamical planar lattice1 and the result agrees with the formulae obtained in Ref. 2 by conformal field theory approach for Potts spins interacting with 2D quantum gravity.- STATISTICAL MECHANICS
- FIELD THEORY: ZERO-DIMENSIONAL
- field theory: scalar
- THERMODYNAMICS: CRITICAL PHENOMENA
- MODEL: POTTS
- FEYNMAN GRAPH: PLANAR
- MATHEMATICAL METHODS: FRACTAL
References(13)
Figures(0)