Anisotropic self-avoiding walks
Anisotropic self-avoiding walks
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各向异性自回避行走
DOI：
10.1063/1.533189
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发表时间：
2000
影响因子：
1.3
通讯作者：
N. Madras
中科院分区：
文献类型：
--
作者：
C. Borgs;J. Chayes;C. King;N. Madras
我们考虑在格子 Zd 上的自回避行走模型，每个 2d 格子方向上的步骤具有不同的权重。我们发现该模型的两点函数的方向相关质量具有三个阶段：所有方向上质量为正；质量相同−∞；以及不同方向的大量不同标志。最后一种可能性只有在权重不对称时才会发生，即，在至少一个坐标中，正方向的权重与负方向的权重不同。这些阶段的边界是精确确定的。我们还证明，如果权重不对称，则典型的 N 步自回避行走其端点之间的距离为 N 阶。
We consider a model of self-avoiding walks on the lattice Zd with different weights for steps in each of the 2d lattice directions. We find that the direction-dependent mass for the two-point function of this model has three phases: mass positive in all directions; mass identically −∞; and masses of different signs in different directions. The final possibility can only occur if the weights are asymmetric, i.e., in at least one coordinate the weight in the positive direction differs from the weight in the negative direction. The boundaries of these phases are determined exactly. We also prove that if the weights are asymmetric then a typical N-step self-avoiding walk has order N distance between its endpoints.