正外磁场下退化Potts模型在Glauber动力学中的亚稳态
摘要
我们考虑具有非零外场和周期边界条件的有限网格图上的铁磁q态Potts模型。系统按照由Metropolis算法描述的Glauber型动力学演化，我们聚焦于低温渐近 regime。我们分析正外磁场的情形。在该能量地形中有个稳定构型和个亚稳态。我们研究了从任意亚稳态到稳定构型的首中时间的渐近行为，当时，在概率、期望和分布意义下。我们还确定了混合时间的指数，并找到了谱间隙的上界和下界。我们也从几何上辨识了从任意亚稳态到唯一稳定构型跃迁的所有最小门的并集与典型轨迹管。
引用
@article{arxiv.2108.04011,
title = {Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics},
author = {Gianmarco Bet and Anna Gallo and Francesca R. Nardi},
journal= {arXiv preprint arXiv:2108.04011},
year = {2024}
}
备注
pg. 50, fig. 15. In this paper we consider, with the same authors, the same model as our previous work arXiv:2105.14335v2, but in a complementary range of parameter values. Thus we write an admin note by marking any known overlaps in advance: sections 1, 2, 3 and appendix in the present paper have some substantial overlap to sections 1, 2, 3 and 5 in the previous paper arXiv:2105.14335v2. arXiv admin note: This version is different than other versions of this paper, and readers should refer to arXiv:2105.14335 for the negative external magnetic field model