猝灭无序对聚合物脱钉转变的平滑效应
Smoothing effect of quenched disorder on polymer depinning transitions
摘要：
我们考虑一般的无序模型钉扎定向聚合物的缺陷线。这一类特别包括$(1+1)$ -维界面润湿模型、DNA变性的无序波兰-Scheraga模型和与平界面相互作用的其他$(1+d)$ -维聚合物。我们还考虑了在选择性界面上吸附的共聚物的情况。在相当一般的条件下，这些模型已知在相图中的某些临界线处具有（去）局域化转变。在这项工作中，我们特别证明，只要无序存在，过渡至少是二阶的，在这个意义上，自由能是可微的临界线，使序参数在过渡连续消失。另一方面，已知相应的非无序模型可以具有一阶（去）局域化转变，具有不连续的一阶导数。因此，我们的结果表明，无序的存在确实有一个平滑的过渡效果。与基于Harris准则的预测的关系进行了讨论。
英文摘要：
We consider general disordered models of pinning of directed polymers on a defect line. This class contains in particular the $(1+1)$--dimensional interface wetting model, the disordered Poland--Scheraga model of DNA denaturation and other $(1+d)$--dimensional polymers in interaction with flat interfaces. We consider also the case of copolymers with adsorption at a selective interface. Under quite general conditions, these models are known to have a (de)localization transition at some critical line in the phase diagram. In this work we prove in particular that, as soon as disorder is present, the transition is at least of second order, in the sense that the free energy is differentiable at the critical line, so that the order parameter vanishes continuously at the transition. On the other hand, it is known that the corresponding non--disordered models can have a first order (de)localization transition, with a discontinuous first derivative. Our result shows therefore that the presence of the disorder has really a smoothing effect on the transition. The relation with the predictions based on the Harris criterion is discussed.
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