地点：科技楼A区311

时间：2024.09.12  14：00

报告人：邓友金 教授   中国科学技术大学

Abstract

We perform large scale simulation of the critical Ising model on a d-dimensionalr hypercube with periodic boundary conditions (d=4, 5, 6, 7)，respectively in the original spin, the Fourtuin-Kasteleyn random-cluster and the loop representation. We find that a complete description of the finite-size scaling behavior at criticality requests simultaneously two sets of critical exponents,respectively from the Gaussian fixed point in the renormalization group and from the Ising model on the complete graph. In addition, we obtain strong numerical evidence that the FK Irandom-cluster representation of the lsing model has simultaneously two upper critical dimensions at (dc=4, du=6). For it is suggested that the largest cluster C1 has a finite-size fractal dimension and the remaining clusters have the fractal dimension. For, all the clusters, except the largest one, have the same tractal structures as the critical uncorrelated percolation clusters in hiah dimensions--e.q.,the finite-size fractal dimension iis . These observations are supported bv (semi-) analvtical results for the so-called random-length random walk as well as the Ising and self-avoid random walk on the complete garaph.