Exact Results for the Universal Area Distribution of Clusters in Percolation, Ising, and Potts Models |
| |
| Authors: | John Cardy Robert M Ziff |
| |
| Institution: | (1) Department of Physics, Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom;(2) All Souls College, Oxford, United Kingdom;(3) Michigan Center for Theoretical Physics and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, 48109-2136 |
| |
| Abstract: | At the critical point in two dimensions, the number of percolation clusters of enclosed area greater than A is proportional to A
–1, with a proportionality constant C that is universal. We show theoretically (based upon Coulomb gas methods), and verify numerically to high precision, that
. We also derive, and verify to varying precision, the corresponding constant for Ising spin clusters, and for Fortuin–Kasteleyn clusters of the Q = 2, 3 and 4-state Potts models. |
| |
| Keywords: | percolation Ising model Potts model universality conformal field theory Coulomb gas methods |
| 本文献已被 SpringerLink 等数据库收录！ |
|
