1. Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; 2. School of Electronic Science and Applied Physics, Hefei University of Technology, Hefei 230009, China; 3. Department of Physics, China University of Mining and Technology, Xuzhou 221116, China
We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, 2013, 87(5): 052107], it is observed that in comparison with dimensionless ratios based on cluster-size distribution, certain wrapping probabilities exhibit weaker finite-size corrections and are more sensitive to the deviation from percolation threshold pc, and thus provide a powerful means for determining pc. We analyze the numerical data of the wrapping probabilities simultaneously such that universal parameters are shared by the aforementioned models, and thus significantly improved estimates of pc are obtained.
S. R. Broadbent and J. M. Hammersley, Percolation processes, Proc. Camb. Philos. Soc , 1957, 53(03): 629 doi: 10.1017/S0305004100032680
2
D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd Ed., London: Taylor & Francis, 1994
3
G. R. Grimmett, Percolation, 2nd Ed., Berlin: Springer, 1999
4
B. Bollobás and O. Riordan, Percolation, Cambridge: Cambridge University Press, 2006 doi: 10.1017/CBO9781139167383
5
B. Nienhuis, Coulomb gas formulation of two-dimensional phase transitions, in: Phase Transition and Critical Phenomena , Vol. 11, edited by C. Domb, M. Green, and J. L. Lebowitz, London: Academic Press, 1987
6
J. L. Cardy, Conformal invariance, in: Phase Transition and Critical Phenomena , Vol. 11, edited by C. Domb, M. Green, and J. L. Lebowitz, London: Academic Press, 1987
7
S. Smirnov and W. Werner, Critical exponents for twodimensional percolation, Math. Res. Lett. , 2001, 8(6): 729 doi: 10.4310/MRL.2001.v8.n6.a4
8
J. W. Essam, Percolation and cluster size, in: Phase Transition and Critical Phenomena, Vol. 2, edited by C. Domb and M. S. Green, New York: Academic Press, 1972
9
X. Feng, Y. Deng, and H. W. J.Bl?te, Percolation transitions in two dimensions, Phys. Rev. E , 2008, 78(3): 031136– and references therein doi: 10.1103/PhysRevE.78.031136
10
C. Ding, Z. Fu, W. Guo, and F. Y. Wu, Critical frontier of the Potts and percolation models on riangular-type and kagome-type lattices (II): Numerical analysis, Phys. Rev. E , 2010, 81(6): 061111– and references therein doi: 10.1103/PhysRevE.81.061111
11
G. Toulouse, Perspectives from the theory of phase transitions, Nuovo Cimento Soc. Ital. Fis. B , 1974, 23(1): 234 doi: 10.1007/BF02737507
12
M. Aizenman and C. M. Newman, Tree graph inequalities and critical behavior in percolation models, J. Stat. Phys. , 1984, 36(1-2): 107 doi: 10.1007/BF01015729
13
T. Hara and G. Slade, Mean-field critical behaviour for percolation in high dimensions, Commun. Math. Phys. , 1990, 128(2): 333 doi: 10.1007/BF02108785
14
J. Wang, Z. Zhou, W. Zhang, T. M. Garoni, and Y. Deng, Bond and site percolation in three dimensions, Phys. Rev. E , 2013, 87(5): 052107 doi: 10.1103/PhysRevE.87.052107
15
Y. Deng and H. W. J.Bl?te, Simultaneous analysis of several models in the three-dimensional Ising universality class, Phys. Rev. E , 2003, 68(3): 036125 doi: 10.1103/PhysRevE.68.036125
16
Y. Deng and H. W. J.Bl?te, Monte Carlo study of the sitepercolation model in two and three dimensions, Phys. Rev. E , 2005, 72(1): 016126 doi: 10.1103/PhysRevE.72.016126
17
S. C. van der Marck, Calculation of percolation thresholds in high dimensions for FCC, BCC and diamond lattices, Int. J. Mod. Phys. C , 1998, 09(04): 529 doi: 10.1142/S0129183198000431
18
A. Silverman and J. Adler, Site-percolation threshold for a diamond lattice with diatomic substitution, Phys. Rev. B , 1990, 42(2): 1369 doi: 10.1103/PhysRevB.42.1369
19
V. A. Vyssotsky, S. B. Gordon, H. L. Frisch, and J. M. Hammersley, Critical percolation probabilities (Bond problem), Phys. Rev. , 1961, 123: 1566 doi: 10.1103/PhysRev.123.1566
20
C. D. Lorenz and R. M. Ziff, Universality of the excess number of clusters and the crossing probability function in threedimensional percolation, J. Phys. A , 1998, 31(40): 8147 doi: 10.1088/0305-4470/31/40/009
21
C. D. Lorenz and R. M. Ziff, Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices, Phys. Rev. E , 1998, 57(1): 230 doi: 10.1103/PhysRevE.57.230
22
R. M. Bradley, P. N. Strenski, and J. M. Debierre, Surfaces of percolation clusters in three dimensions, Phys. Rev. B , 1991, 44(1): 76 doi: 10.1103/PhysRevB.44.76
23
D. S. Gaunt and M. F. Sykes, Series study of random percolation in three dimensions, J. Phys. A , 1983, 16(4): 783 doi: 10.1088/0305-4470/16/4/016
24
R. M. Ziff, S. R. Finch, and V. S. Adamchik, Universality of finite-size corrections to the number of critical percolation clusters, Phys. Rev. Lett. , 1997, 79(18): 3447 doi: 10.1103/PhysRevLett.79.3447
