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Scaling relations for two-dimensional Ising percolation. (English) Zbl 1321.82013

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

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B43 Percolation
82B27 Critical phenomena in equilibrium statistical mechanics
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