Incipient infinite cluster in 2D Ising percolation
Yasunari Higuchi, Kazunari Kinoshita, Masato Takei, and Yu Zhang
TL;DR
This paper constructs the incipient infinite cluster measure in 2D Ising percolation near criticality, revealing geometric properties and extending results to the triangular lattice.
Contribution
It introduces a construction of the IIC measure in 2D Ising percolation at criticality, providing new insights into its geometric structure.
Findings
Construction of IIC measure in 2D Ising percolation
Geometric properties of the IIC
Extension of results to the triangular lattice
Abstract
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.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods