Lee-Yang 性质与高斯乘性混沌
数学物理
2018-08-22 v3 math.MP
摘要
某些矩生成函数仅具有纯虚零点的 Lee-Yang 性质，对具有单分量自旋的 Ising 型模型和具有双分量自旋的 XY 模型均成立。Villain 模型和复高斯乘性混沌是与 XY 模型类似的双分量系统，且与高斯自由场相关。虽然已知 Lee-Yang 性质在第一种情况下普遍成立，但我们证明其在第二种情况下并不成立。我们的证明基于两个具有普遍意义的定理，这些定理将 Lee-Yang 性质与分布尾部行为联系起来。
引用
@article{arxiv.1708.08820,
title = {Lee-Yang Property and Gaussian multiplicative chaos},
author = {Charles M. Newman and Wei Wu},
journal= {arXiv preprint arXiv:1708.08820},
year = {2018}
}
备注
We changed the title to emphasize Gaussian multiplicative chaos. Theorem 11, giving criteria for when some zeros are not purely imaginary, has been considerably strengthened. This yields a correspondingly improved result for continuum complex Gaussian multiplicative chaos in Proposition 18