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Percolation in the two-dimensional Ising model
Tao Chen1,2, Jinhong Zhu1, Wei Zhong3
1University of Science and Technology of China, Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, Hefei 230026, People's Republic of China.
Abstract:
The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds, with probability p, between any pair of parallel spins within an extended range beyond nearest neighbors. At the Ising criticality, we observe two percolation transitions as p increases: starting from a disordered phase with only small clusters, the percolation system enters into a stable critical phase that persists over a wide range p_{c_{1}}
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