混合偶自旋模型中溫度和亂度的渾沌態

Abstract

在Sherrington-Kirkpatrick model的渾沌問題中，如果能夠透過增加擾動來簡化模型的行為，我們稱之為渾沌。 在這個研究中，我們想了解，當我們輕微改變溫度或亂度其中一個參數的情況下，兩個mixed even-spin models之間的行為。我們用新的Ghirlanda-Guerra identities以及Guerra's bound的推廣來證明這兩個系統中，分別獨立抽出一個樣本，這兩個樣本重疊部分比率的極限分佈會集中於一個常數。

In the chaos problem of the Sherrington-Kirkpatrick model, we say that there is chaos if the behavior of the model becomes much simpler after adding the perturbation. In this study, we concerned about the behavior of the coupled system that are both mixed even-spin models when one of the parameter of temperature or the parameter of disorder is slightly different. We use the new Ghirlanda-Guerra identities and the extended Guerra's bound to prove that the limiting distribution of the overlap between two independently sampled configurations from, respectively, is concentrated around a constant.