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Properties Of The Ising Magnet Confined In A Corner Geometry

机译：限制在角几何形状中的Ising磁铁的性质

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摘要

The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ± h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field -h acts. For temperatures T less than the critical temperature T_c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T_f (h) runs from the upper left corner to the lower right corner, while for T < T_f (h) this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T = T_f (h) the magnetization profile m(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w ∝ L, while for T > T_f (h) it scales as w ∝ L~(1/2). The distribution P(l) of the interface position l (measured along the z-direction from the corners) decays exponentially for T < T_f (h) from either corner, is essentially flat for T = T_f (h), and is a Gaussian centered at the middle of the diagonal for T > T_f (h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.
机译：通过蒙特卡洛模拟研究了具有最邻近铁磁交换的伊辛方格的性质，该方格被限制在一个角几何中。施加边界磁场±h的自由边界条件，即，在左下角处结束的两个边界行处，场+ h起作用，而在右上角处结束的两个边界行处，场-h起作用。当温度T小于主体的临界温度T_c时，该边界条件导致形成两个磁化方向相反的畴，并通过一个界面进行分隔，对于T来说，该界面大于填充转变温度T_f（h）从左上角到右下角，而对于T T_f（h）则按比例缩放如w ∝ L〜（1/2）。界面位置l的分布P（l）（从拐角沿z方向测量）从任一拐角开始对T T_f（h），位于对角线的中间。与Ising模型的薄膜几何形状中临界润湿的发现不同，Monte Carlo的角润湿结果与理论预测非常吻合。

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