非局部双轴离散周长的等周不等式
Isoperimetric inequality for nonlocal bi-axial discrete perimeter
AI总结：
本文首次提出非局部双轴离散周长的等周不等式问题，并将其与长程双轴伊辛模型的不稳定行为研究联系起来。
摘要：
在本文中，我们首次解决了非局部离散等周问题。我们考虑了一个经典的周长的推广，称为非局部双轴离散周长，其中不仅多格多边形P的外部边界贡献于周长，而且所有内部和外部组件也贡献于周长。此外，我们在固定面积n的多格多边形类中找到并 characterize 其极小值。此外，我们解释了非局部离散等周问题的解如何与长程双轴伊辛模型的不稳定行为的严格研究相关联。
英文摘要：
In the present manuscript we address and solve for the first time a nonlocal discrete isoperimetric problem. We consider indeed a generalization of the classical perimeter, what we call a nonlocal bi-axial discrete perimeter, where, not only the external boundary of a polyomino $\mathcal{P}$ contributes to the perimeter, but all internal and external components of $\mathcal{P}$. Furthermore, we find and characterize its minimizers in the class of polyominoes with fixed area $n$. Moreover, we explain how the solution of the nonlocal discrete isoperimetric problem is related to the rigorous study of the metastable behavior of a long-range bi-axial Ising model.
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