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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

Authors :
Bhadola, P.
Garg, I.
Deo, N.
Source :
Nuclear Physics B. May2013, Vol. 870 Issue 2, p384-396. 13p.
Publication Year :
2013

Abstract

Abstract: 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 for large N (size of matrix, ) to for small N (). 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. [Copyright &y& Elsevier]

Details

Language :
English
ISSN :
05503213
Volume :
870
Issue :
2
Database :
Academic Search Index
Journal :
Nuclear Physics B
Publication Type :
Academic Journal
Accession number :
85583553
Full Text :
https://doi.org/10.1016/j.nuclphysb.2013.01.010