Structure combinatorics and thermodynamics of a matrix model with Penner interaction inspired by interacting RNA
Structure combinatorics and thermodynamics of a matrix model with Penner interaction inspired by interacting RNA
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DOI：
10.1016/j.nuclphysb.2013.01.010
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
P. Bhadola;I. Garg;N. Deo
中科院分区：
文献类型：
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作者：
P. Bhadola;I. Garg;N. Deo
在本文中，我们研究了相互作用的RNA折叠和结构组合的随机矩阵模型中的对数Penner型非线性相互作用。Penner相互作用最早出现在对穿透表面模数空间的研究中，并首次应用于RNA折叠。利用正交多项式方法，得到了母函数的精确解析公式。由生成函数导出的RNA链的给定长度L的配分函数列举了所有可能的拓扑结构和配对。得到了配分函数和渐近的大长度分布函数，并表明从L−3/2到L−1/2，对于大N(矩阵的大小，N&gT；L)，对于小N(N≪L)，二级结构贡献的临界指数发生了变化。用该模型计算的精确解析结果可用于估算大相互作用强度下的比热-温度曲线。特别是，比热的二阶导数表现出明显的变化，由大N的单峰函数变为小N的双峰函数。
In this manuscript, we study the logarithmic Penner type nonlinear interaction in the random matrix model for interacting RNA folding and structure combinatorics. The Penner interaction originally appeared in the studies of moduli space of punctured surfaces and has been applied here in the context of RNA folding for the first time. An exact analytic formula for the generating function is derived using the orthogonal polynomial method. The partition function for a given length L of the RNA chain, derived from the generating function enumerates all possible topological structures as well as the pairings. The partition function and the asymptotic large length distribution functions are found and show a change in the critical exponent of the secondary structure contribution from L−3/2for large N (size of matrix, N>L) to L−1/2for small N (N≪L). The exact analytic results calculated in the proposed model allow evaluation of the specific heat versus T curve for large interaction strength. In particular, the second derivative of specific heat shows a striking behavior, changing from single peaked function for large N to a double peak for small N.