Incipient Infinite Cluster in 2D Ising Percolation

Yasunari Higuchi, Kasunari Kinoshita, Masato Takei, Fuxi Zhang

2014, v.20, Issue 2, 73-182


We consider the percolation problem in the high-temperature Ising model on the two-dimensional square lattice at or near critical external fields. The incipient infinite cluster (IIC) measure in the sense of Kesten is constructed. As a consequence, we can obtain some geometric properties of IIC. The result holds also for the triangular lattice.

Keywords: percolation,Ising model,incipient infinite cluster


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