关于相关高斯环境中无序对钉扎模型影响的评述
数学物理
2013-11-07 v2 math.MP
概率论
摘要
我们研究了随机钉扎模型，其环境为呈现幂律衰减相关的高斯环境，衰减指数 a>0。我们评论了退火（即对无序进行平均）模型，该模型绝非平凡，并讨论了无序对系统临界性质的影响。我们证明，只要相关衰减足够快（a>2），退火临界指数 \nu^{ann} 就与纯系统临界指数 \nu^{pur} 相同。若相关是可和的（a>1），我们还证明了无序相变至少为 2 阶，表明当 \nu^{pur}<2 时无序是相关的。若相关不可和（a<1），我们证明相变消失。
引用
@article{arxiv.1301.5307,
title = {Comments on the Influence of Disorder for Pinning Model in Correlated Gaussian Environment},
author = {Quentin Berger},
journal= {arXiv preprint arXiv:1301.5307},
year = {2013}
}
备注
23 pages, 1 figure Modifications in v2 (outside minor typos): Assumption 1 on correlations has been simplified for more clarity; Theorem 4 has been improved to a more general underlying renewal distribution; Remark 2.1 added, on the assumption on the correlations in the summable case