$d\geq 2$ 维伊辛自旋玻璃的有限温度相变
无序系统与神经网络
2022-09-21 v4 统计力学
数学物理
math.MP
摘要
人们相信 伊辛自旋玻璃在维度 中于有限温度下不发生有序。然而，利用图表示和轮廓论证，我们严格证明了在 中存在有限温度相变，且 。在图表示中，低温相允许多个无限团簇共存，每个团簇具有刚性对齐的自旋重叠态。这些团簇彼此呈负关联，且在不破坏任何整体对称性的情况下具有熵稳定性。它们可在大多数图结构和无序测度中出现。
引用
@article{arxiv.2105.01188,
title = {A Finite-temperature Phase Transition for the Ising Spin-glass in $d\geq 2$},
author = {Yan Ru Pei and Massimiliano Di Ventra},
journal= {arXiv preprint arXiv:2105.01188},
year = {2022}
}
备注
The proof of the finitude of zero-energy contours in Appendix D.2 contains a technical error, where we failed to notice that opening a red bond in any of the four quadrants can possibly restrict opening of any blue bonds in the contour. This means that the probability that the contour is zero-energy (no blue-bonds) cannot be bounded exponentially, thus the result does not immediately follow