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Geometric Upper Critical Dimensions of the Ising Model |
| Sheng Fang1,2, Zongzheng Zhou3*, and Youjin Deng1,2,4* |
1Hefei National Research Center for Physical Sciences at the Microscales, University of Science and Technology of China, Hefei 230026, China
2MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China
3ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics, Monash University, Clayton, Victoria 3800, Australia
4Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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Sheng Fang, Zongzheng Zhou, and Youjin Deng 2022 Chin. Phys. Lett. 39 080502 |
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Abstract The upper critical dimension of the Ising model is known to be $d_{\rm c}=4$, 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 $(d_{\rm c}=4,~d_{\rm p}=6)$, and critical clusters for $d \geq d_{\rm p}$, 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.
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Received: 12 June 2022
Express Letter
Published: 08 July 2022
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