EXACT RESULTS AT THE TWO-DIMENSIONAL PERCOLATION POINT

作者: P. Kleban , R. M. Ziff

DOI: 10.1103/PHYSREVB.57.R8075

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摘要: We derive exact expressions for the excess number of clusters b and cumulants b_n a related quantity at 2-D percolation point. High-accuracy computer simulations are in accord with our predictions. is finite-size correction to Temperley-Lieb or Baxter-Temperley-Ashley formula per site n_c infinite system limit; bn correct bulk cumulants. universal, thus depend only on system's shape. Higher-order corrections show no apparent dependence fractional powers size.

参考文章(22)
Amnon Aharony, J-P. Hovi, Comment on "Spanning probability in 2D percolation" Physical Review Letters. ,vol. 72, pp. 1941- 1941 ,(1994) , 10.1103/PHYSREVLETT.72.1941
J.-P. Hovi, Amnon Aharony, Scaling and universality in the spanning probability for percolation Physical Review E. ,vol. 53, pp. 235- 253 ,(1996) , 10.1103/PHYSREVE.53.235
Vl.S. Dotsenko, V.A. Fateev, Conformal algebra and multipoint correlation functions in 2D statistical models Nuclear Physics. ,vol. 240, pp. 312- 348 ,(1984) , 10.1016/0550-3213(84)90269-4
J L Cardy, Critical percolation in finite geometries Journal of Physics A. ,vol. 25, ,(1992) , 10.1088/0305-4470/25/4/009
P. di Francesco, H. Saleur, J. B. Zuber, Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models Journal of Statistical Physics. ,vol. 49, pp. 57- 79 ,(1987) , 10.1007/BF01009954
Haru T. Pinson, Critical percolation on the torus Journal of Statistical Physics. ,vol. 75, pp. 1167- 1177 ,(1994) , 10.1007/BF02186762
Robert Langlands, Philippe Pouliot, Yvan Saint-Aubin, Conformal invariance in two-dimensional percolation Bulletin of the American Mathematical Society. ,vol. 30, pp. 1- 61 ,(1994) , 10.1090/S0273-0979-1994-00456-2