The interface of the Ising model and the Brownian sheet |
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Authors: | Koji Kuroda Hiroko Manaka |
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Institution: | (1) Department of Mathematics, Keio University, Japan |
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Abstract: | We study the limit theorem related to the interface of the three-dimensional Ising model. Dobrushin proved that the interface does not fluctuate and becomes rigid for sufficiently large. We define the random fieldX
L
(t, s), 0t, s1, on the interface, and prove that XL(t, s) converges to the Brownian sheet as L for sufficiently large, whereL denotes the size of the system. This result does not mean that the interface itself converges to the Brownian sheet. |
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Keywords: | Interface Ising model standard wall Brownian sheet |
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