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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(dc = 4, dp = 6), and critical clusters for d ≥ dp, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric propertie... 相似文献
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