具有线性外相互作用的RNA矩阵模型的标度、相变和亏格分布函数
Scaling, phase transition and genus distribution functions in matrix models of RNA with linear external interactions
摘要：
在RNA随机矩阵模型配分函数的作用下引入线性外扰动[G. Vernizzi，H. Orland和A. Zee，Phys. Rev. Lett. 94，168103（2005）]。可以看出，（i）。所述扰动区分配对和未配对碱基，因为当扰动参数$α$接近1（$α$是在配分函数作用下原始项和扰动项的相互作用强度的比率）时，存在从未配对和配对碱基结构（$0 \leq α< 1$）到完全配对碱基结构（$α=1$）的结构变化，（ii）。对于小的偶数和奇数长度$L$，亏格分布表现出小的差异，（iii）。所述线性相互作用矩阵模型的配分函数通过缩放公式与RNA的随机矩阵模型的重新缩放的配分函数相关，（iv）。将自由能和比热作为$L$、$α$和温度$T$的函数绘制，并且将它们相对于$α$的一阶导数作为$α$的函数绘制。自由能显示对于奇数（小和大）长度在$α=1$处的相变，并且对于偶数长度，随着包括更多的伪结（即对于大长度），在$α=1$处的相变变得越来越尖锐。
英文摘要：
A linear external perturbation is introduced in the action of the partition function of the random matrix model of RNA [G. Vernizzi, H. Orland and A. Zee, Phys. Rev. Lett. 94, 168103 (2005)]. It is seen that (i). the perturbation distinguishes between paired and unpaired bases in that there are structural changes, from unpaired and paired base structures ($0 \leq α< 1$) to completely paired base structures ($α=1$), as the perturbation parameter $α$ approaches 1 ($α$ is the ratio of interaction strengths of original and perturbed terms in the action of the partition function), (ii). the genus distributions exhibit small differences for small even and odd lengths $L$, (iii). the partition function of the linear interacting matrix model is related via a scaling formula to the re-scaled partition function of the random matrix model of RNA, (iv). the free energy and specific heat are plotted as functions of $L$, $α$ and temperature $T$ and their first derivative with respect to $α$ is plotted as a function of $α$. The free energy shows a phase transition at $α=1$ for odd (both small and large) lengths and for even lengths the transition at $α=1$ gets sharper and sharper as more pseudoknots are included (that is for large lengths).
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