广义Poland-Scheraga模型中的无序和变性相变
Disorder and denaturation transition in the generalized Poland-Scheraga model
摘要：
我们研究广义波兰Scheraga模型，这是在生物物理文献中使用的DNA变性过渡模型，在这种情况下，两条链被允许是非互补的（并有不同的长度）。最近从数学的角度研究了齐次模型，Giacomin，Khatib（Stoch.申请程序，2017），通过$2$维更新方法，具有循环指数$2+α$（${α>0}$）：发现其经历$ν= \min(1,α)^{-1}$阶的定域/离域相变，以及-通常-其他相变。在本文中，我们转向无序模型，我们解决的问题，无序的变性相变的影响，也就是说，是否添加任意少量的无序（即不均匀性）影响的临界特性，这种转变。我们的结果与Harris对$d$维无序系统（这里是$d=2$）的预测一致.首先，我们证明了当$α<1$（即$ν>d/2$），那么无序是无关紧要的：淬火和退火的临界点是相等的，无序变性相变也是有序的$ν=α^{-1}$。另一方面，当$α>1$，无序是相关的：我们证明，淬火和退火的临界点不同。此外，我们讨论了一些开放的问题，特别是平滑现象，预计将进入游戏时，无序是相关的。
英文摘要：
We investigate the generalized Poland-Scheraga model, which is used in the bio-physical literature to model the DNA denaturation transition, in the case where the two strands are allowed to be non-complementary (and to have different lengths). The homogeneous model was recently studied from a mathematical point of view in Giacomin, Khatib (Stoch. Proc. Appl., 2017), via a $2$-dimensional renewal approach, with a loop exponent $2+α$ (${α>0}$): it was found to undergo a localization/delocalization phase transition of order $ν= \min(1,α)^{-1}$, together with -- in general -- other phase transitions. In this paper, we turn to the disordered model, and we address the question of the influence of disorder on the denaturation phase transition, that is whether adding an arbitrarily small amount of disorder (i.e. inhomogeneities) affects the critical properties of this transition. Our results are consistent with Harris' predictions for $d$-dimensional disordered systems (here $d=2$). First, we prove that when $α<1$ (i.e. $ν>d/2$), then disorder is irrelevant: the quenched and annealed critical points are equal, and the disordered denaturation phase transition is also of order $ν=α^{-1}$. On the other hand, when $α>1$, disorder is relevant: we prove that the quenched and annealed critical points differ. Moreover, we discuss a number of open problems, in particular the smoothing phenomenon that is expected to enter the game when disorder is relevant.
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