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arXiv · 2201.12954

Geometric Upper Critical Dimensions of the Ising Model

Sheng Fang·Zongzheng Zhou·Youjin Deng
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Abstract

The upper critical dimension of the Ising model is known to be $d_c=4$, above which critical behavior is regarded as 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 $d \geq d_p$, 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.

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Sheng Fang, Zongzheng Zhou, Youjin Deng. 2022-01-31. Geometric Upper Critical Dimensions of the Ising Model. https://doi.org/10.1088/0256-307x%2F39%2F8%2F080502

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