三角格点上无根森林的重整化流
Renormalization flow for unrooted forests on a triangular lattice
摘要：
在小温度展开下，计算了N=-1的三角格子上具有O（N）不变性的σ模型的两圈重整化常数和第一非普适项β函数的三圈系数.相应的格拉斯曼理论的配分函数是，对于负温度，无根森林在这样的晶格上的生成函数，其中温度作为森林中树木数量的化学势。为了计算费曼图，我们将坐标空间方法推广到三角晶格。
英文摘要：
We compute in small temperature expansion the two-loop renormalization constants and the three-loop coefficient of the beta-function, that is the first non-universal term, for the sigma-model with O(N) invariance on the triangular lattice at N=-1. The partition function of the corresponding Grassmann theory is, for negative temperature, the generating function of unrooted forests on such a lattice, where the temperature acts as a chemical potential for the number of trees in the forest. To evaluate Feynman diagrams we extend the coordinate space method to the triangular lattice.
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