Janssen H K, Stenull O, Oerding K
Institut für Theoretische Physik III, Heinrich-Heine-Universität, Universitätsstrasse 1, 40225 Düsseldorf, Germany.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jun;59(6):R6239-42. doi: 10.1103/physreve.59.r6239.
We present an alternative view of Feynman diagrams for the field theory of random resistor networks, in which the diagrams are interpreted as being resistor networks themselves. This simplifies the field theory considerably as we demonstrate by calculating the fractal dimension D(B) of the percolation backbone to three loop order. Using renormalization group methods we obtain D(B)=2+epsilon/21-172epsilon(2)/9261+2epsilon(3)[-74 639+22 680zeta(3)]/4 084 101, where epsilon=6-d with d being the spatial dimension and zeta(3)=1.202 057... .
我们给出了用于随机电阻网络场论的费曼图的另一种观点，其中这些图被解释为它们自身就是电阻网络。正如我们通过计算逾渗骨架的分形维数(D(B))到三圈阶次所证明的，这极大地简化了场论。使用重整化群方法，我们得到(D(B)=2+\epsilon/21 - 172\epsilon(2)/9261 + 2\epsilon(3)[-74639 + 22680\zeta(3)]/4084101)，其中(\epsilon = 6 - d)，(d)为空间维度，(\zeta(3)=1.202057\cdots) 。
