摘要
The upper critical dimension of the Ising model is known to be dc=4,above which critical behavior is regarded to be trivial.We hereby argue from extensive simulations that,in the random-cluster representation,the Ising model simultaneously exhibits two upper critical dimensions at(d_(c)=4,d_(p)=6),and critical clusters for d≥d_(p),except the largest one,are governed by exponents from percolation universality.We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs.Our findings significantly advance the understanding of the Ising model,which is a fundamental system in many branches of physics.
作者
Sheng Fang
Zongzheng Zhou
Youjin Deng
方胜;周宗政;邓友金(Hefei National Research Center for Physical Sciences at the Microscales,University of Science and Technology of China,Hefei 230026,China;MinJiang Collaborative Center for Theoretical Physics,College of Physics and Electronic Information Engineering,Minjiang University,Fuzhou 350108,China;ARC Centre of Excellence for Mathematical and Statistical Frontiers(ACEMS),School of Mathematics,Monash University,Clayton,Victoria 3800,Australia;Shanghai Research Center for Quantum Sciences,Shanghai 201315,China)
