粘性墙上具有单交互和双交互的两次友好行走的精确解
Exact solution of two friendly walks above a sticky wall with single and double interactions
摘要：
我们发现，并分析，两个友好的定向行走，建模聚合物，通过接触相互作用与墙壁相互作用的精确解。我们特别考虑开始和结束在一起的两个行走，以模仿多边形。我们研究了一个一般的模型，其中一个单独的相互作用参数被分配到两个聚合物同时接触壁的配置，并调查这个参数对问题的可积性的影响。我们找到一个精确的解决方案的模型的生成函数，并提供了一个完整的分析的相图，承认三个阶段与一个一阶和两个二阶过渡线之间的这些阶段。我们认为，一个物理上可实现的模型将看到两个相变的温度降低。
英文摘要：
We find, and analyse, the exact solution of two friendly directed walks, modelling polymers, which interact with a wall via contact interactions. We specifically consider two walks that begin and end together so as to imitate a polygon. We examine a general model in which a separate interaction parameter is assigned to configurations where both polymers touch the wall simultaneously, and investigate the effect this parameter has on the integrability of the problem. We find an exact solution of the generating function of the model, and provide a full analysis of the phase diagram that admits three phases with one first-order and two second-order transition lines between these phases. We argue that one physically realisable model would see two phase transitions as the temperature is lowered.
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