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 Isin...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.展开更多
文摘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.
