Behavior of the two-dimensional Ising model at the boundary of a half-infinite cylinder

Yvan Saint-Aubin; Louis-Pierre Arguin; Hassan Aurag

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arXiv · 0909.4041

Behavior of the two-dimensional Ising model at the boundary of a half-infinite cylinder

Yvan Saint-Aubin·Louis-Pierre Arguin·Hassan Aurag

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Abstract

The two-dimensional Ising model is studied at the boundary of a half-infinite cylinder. The three regular lattices (square, triangular and hexagonal) and the three regimes (sub-, super- and critical) are discussed. The probability of having precisely 2n spinflips at the boundary is computed as a function of the positions k_i's, i=1,..., 2n, of the spinflips. The limit when the mesh goes to zero is obtained. For the square lattice, the probability of having 2n spinflips, independently of their position, is also computed. As a byproduct we recover a result of De Coninck showing that the limiting distribution of the number of spinflips is Gaussian. The results are obtained as consequences of Onsager's solution and are rigorous.

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Yvan Saint-Aubin, Louis-Pierre Arguin, Hassan Aurag. 2009-09-22. Behavior of the two-dimensional Ising model at the boundary of a half-infinite cylinder. https://arxiv.org/abs/0909.4041

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