摘要
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.Reu.E 72,016126(2005)]using the disjoint-set data structure,and simulate a cylindrical geometry Ld^-1×∞,with the linear size up to L=512 for 4D and 128 for 5D.We determine with 1 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/v=1.4610(12)for 4D and 1/v=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.
基金
We dedicate this work to Fred(Fa-Yueh)Wu who passed away on January 21,2020.Known internationally for his contributions in statistical mechanics and solid state physics,Wu was a professor at Northeastern University for 39 years until his retirement in 2006 as Matthews Distinguished University Professor of Physics.His seminal review article on the Potts model[7]has benefitted several generations of statistical physicists.His broad interests in influence on his research community were illustrated by the special issue[56]that one of us(J.L.J.)co-edited for his 80 years birthday.In 2004,Wu was a member of the doctoral dissertation committee of another of us(Y.D.),and subsequently gave him a lot of encouragement throughout his academic career.We are indebted to Romain Couvreur for valuable discussions.Y.D.acknowledges the support by the National Natural Science Foundation of China(Grant No.11625522)
the Ministry of Science and Technology of China(Grant No.2016YFA0301604).J.L.J.acknowledges support of the European Research Council through the Advanced Grant NuQFT.Simulations were carried out at the Supercomputing Center of the University of Science and Technology of China.
