Macroscopic loops in the loop $O(n)$ model at Nienhuis' critical point,Journal of the European Mathematical Society

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Macroscopic loops in the loop $O(n)$ model at Nienhuis' critical point
Journal of the European Mathematical Society ( IF 2.5 ) Pub Date : 2020-10-21 , DOI: 10.4171/jems/1012
Hugo Duminil-Copin ₁ , Alexander Glazman ₂ , Ron Peled ₃ , Yinon Spinka ₄

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The loop $O(n)$ model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n)$ model. It has been predicted by Nienhuis that for $0\le n\le 2$ the loop $O(n)$ model exhibits a phase transition at a critical parameter $x_c(n)=\tfrac{1}{\sqrt{2+\sqrt{2-n}}}$. For $0

中文翻译：

Nienhuis 临界点处的循环 $O(n)$ 模型中的宏观循环

循环$O(n)$模型是六边形点阵上不相交循环的随机集合的模型，被认为与自旋$O(n)$模型属于相同的通用性类。Nienhuis 已经预测，对于 $0\le n\le 2$，回路 $O(n)$ 模型在关键参数 $x_c(n)=\tfrac{1}{\sqrt{2+ \sqrt{2-n}}}$。0 美元

更新日期：2020-10-21

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