Summary
We prove that at low enough temperatures the phase separation line, when it is suitably normalized, converges almost surely in a suitable probability space to the path of a one-dimensional Brownian bridge. The convergence is in the sense of the distance between compact sets in [0, 1] ×R 1.
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Dedicated to Professor Leopold Schmetterer on the occasion of his 60th birthday
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Higuchi, Y. On some limit theorems related to the phase separation line in the two-dimensional ising model. Z. Wahrscheinlichkeitstheorie verw Gebiete 50, 287–315 (1979). https://doi.org/10.1007/BF00534152
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DOI: https://doi.org/10.1007/BF00534152