论文标题
在沿着硬墙吸附的自相互作用行走的倒塌阶段的表面过渡
Surface transition in the collapsed phase of a self-interacting walk adsorbed along a hard wall
论文作者
论文摘要
本文专用于二维相互作用的部分定向的自我避免行走，以限制在上半程的计划中，并与水平轴相互作用。该模型是在\ cite {f90}中引入的，以研究浸入较差的溶剂中的均聚物的行为，并沿着水平硬壁吸附。众所周知，它会在扩展相之间发生崩溃的过渡，在该相位的内部，聚合物的典型构型具有较大的水平延伸（与它们的总尺寸相当），并且在其中折叠的相位看起来像是球体。 在本文中，我们严格地确定在折叠阶段的内部，在吸附的胶囊方向上发生了表面转变，在该方案中，将球的底层层固定在硬壁上，而无吸引力的机制在该方案中偏离了墙壁。为了证明这种表面过渡的存在并表现出其相关的临界曲线，我们为模型的稍微简化版本显示了分区函数的一些尖锐渐近曲线。
The present paper is dedicated to the 2-dimensional Interacting Partially Directed Self Avoiding Walk constrained to remain in the upper-half plan and interacting with the horizontal axis. The model has been introduced in \cite{F90} to investigate the behavior of a homopolymer dipped in a poor solvent and adsorbed along a horizontal hard wall. It is known to undergo a collapse transition between an extended phase, inside which typical configurations of the polymer have a large horizontal extension (comparable to their total size), and a collapsed phase inside which the polymer looks like a globule. In the present paper, we establish rigorously that inside the collapsed phase, a surface transition occurs between an adsorbed-collapsed regime where the bottommost layer of the globule is pinned at the hard wall, and a desorbed-collapsed regime where the globule wanders away from the wall. To prove the existence of this surface transition and exhibit its associated critical curve, we display some sharp asymptotics of the partition function for a slightly simplified version of the model.
