Incipient infinite cluster in 2D Ising percolation

Yasunari Higuchi, Kazunari Kinoshita, Masato Takei, Yu Zhang

Published 2013-07-27Version 1

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.