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Crossing probabilities on same-spin clusters in the two-dimensional Ising model

Ervig Lapalme·Yvan Saint-Aubin
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Abstract

Probabilities of crossing on same-spin clusters, seen as order parameters, have been introduced recently for the critical 2d Ising model by Langlands, Lewis and Saint-Aubin. We extend Cardy's ideas, introduced for percolation, to obtain an ordinary differential equation of order 6 for the horizontal crossing probability pih. Due to the identity pih(r)+pih(1/r)=1, the function pih must lie in a 3-dimensional subspace. New measurements of pih are made for 40 values of the aspect ratio r (r in [0.1443,6.928]). These data are more precise than those obtained by Langlands et al as the 95%-confidence interval is brought to 4x10^{-4}. A 3-parameter fit using these new data determines the solution of the differential equation. The largest gap between this solution and the 40 data is smaller than 4x10^{-4}. The probability pihv of simultaneous horizontal and vertical crossings is also treated.

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Ervig Lapalme, Yvan Saint-Aubin. 2000-05-11. Crossing probabilities on same-spin clusters in the two-dimensional Ising model. https://doi.org/10.1088/0305-4470%2F34%2F9%2F302

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