Basic techniques in two-dimensional critical Ising percolation with investigation of scaling relations

2010/10/08 by Yasunari Higuchi, Masato Takei, Higuchi, Yasunari +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1010.1586

openalex publication_date 2010/10/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider the percolation problem in the high-temperature Ising model on the two-dimensional square lattice at/near critical external fields. We show that all scaling relations, except a single hyperscaling relation, hold under the power law assumptions for the one-arm path and four-arm paths.

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• Incipient infinite cluster in 2D Ising percolation

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