Fluid Interfaces in the 3D Ising Model as a Dilute Gas of Handles

Details Fluid Interfaces in the 3D Ising Model as a Dilute Gas of Handles Fluid Interfaces in the 3D Ising Model as a Dilute Gas of Handles

1994-07-04

arxiv.org/abs/cond-mat/9407012v1

Physics

Condensed Matter

15 pages, Latex and 10 ps figs (uuencoded file) DFTT 27/94

Scientific paper

We study the topology of fluid interfaces in the 3D Ising model in the rough phase. It turns out that such interfaces are accurately described as dilute gases of microscopic handles, and the stiffness of the interface increases with the genus. The number of configurations of genus $g$ follows a Poisson-like distribution. The probability per unit area for creating a handle is well fitted in a wide range of the inverse temperature $\beta$ near the roughening point by an exponentially decreasing function of $\beta$. The procedure of summing over all topologies results in an effective interface whose squared width scales logarithmically with the lattice size.

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