$N$-cluster correlations in four- and five-dimensional percolation

Xiaojun Tan (1) , Youjin Deng (1) , Jesper Lykke Jacobsen (2, 3)

1 USTC - University of Science and Technology of China [Hefei]
2 Champs Aléatoires et Systèmes hors d'Équilibre
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We study N-cluster correlation functions in four- and five-dimensional (4D and 5D) bond percolation by extensive Monte Carlo simulation. We reformulate the transfer Monte Carlo algorithm for percolation [Phys. Rev. E72, 016126 (2005)] using the disjoint-set data structure, and simulate a cylindrical geometry L$^{d−1}$ × ∞, with the linear size up to L = 512 for 4D and 128 for 5D. We determine with a high precision all possible N-cluster exponents, for N = 2 and 3, and the universal amplitude for a logarithmic correlation function. From the symmetric correlator with N=2, we obtain the correlation-length critical exponent as 1/ν=1.4610(12) for 4D and 1/ν=1.737(2) for 5D, significantly improving over the existing results. Estimates for the other exponents and the universal logarithmic amplitude have not been reported before to our knowledge. Our work demonstrates the validity of logarithmic conformal field theory and adds to the growing knowledge for high-dimensional percolation.

Mots clés: critical exponents; percolation; logarithmic conformal field theory; Monte Carlo algorithm

Domaines: Mécanique statistique [cond-mat.stat-mech]

Xiaojun Tan, Youjin Deng, Jesper Lykke Jacobsen. $N$-cluster correlations in four- and five-dimensional percolation. Frontiers of Physics, 2020, 15 (4), pp.41501. ⟨10.1007/s11467-020-0972-6⟩. ⟨hal-02892952⟩