渗流变分问题：刚性自旋系统
Variational problems with percolation: rigid spin systems
摘要：
在本文中，我们描述了刚性自旋晶格能的渐近行为，表现出一个连续的界面极限能量作为缩放到零的晶格间距。在渗流阈值以下，该极限并不是微不足道的：它可以由被界面分离的两相来表征。该界面处的宏观表面张力通过第一次通过渗透公式定义，与正方形晶格上的化学距离相关。我们还证明了一个连续性结果，即刚性自旋系统的均匀化是椭圆随机均匀化的一个极限情形。
英文摘要：
In this paper we describe the asymptotic behavior of rigid spin lattice energies by exhibiting a continuous interfacial limit energy as scaling to zero the lattice spacing. The limit is not trivial below a percolation threshold: it can be characterized by two phases separated by an interface. The macroscopic surface tension at this interface is defined through a first-passage percolation formula, related to the chemical distance on the square lattice. We also show a continuity result, that is the homogenization of rigid spin system is a limit case of the elliptic random homogenization.
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