Structure combinatorics and thermodynamics of a matrix model with Penner interaction inspired by interacting RNA

Bhadola, Pradeep; Garg, I.; Deo, Nivedita

doi:10.1016/j.nuclphysb.2013.01.010

Cited by 11 publications

(15 citation statements)

References 43 publications

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“…This model has been applied to derive new asymptotics for the generalized Laguerre polynomials [6], to the study of structural glasses in the high temperature phase [5] and to the study of interacting RNA folding and structure combinatorics [10].…”

Section: The Z 2 -Symmetric Gaussian Penner Modelmentioning

confidence: 99%

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Partition functions and the continuum limit in Penner matrix models

Álvarez¹,

Alonso²,

Медина³

2014

J. Phys. A: Math. Theor.

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Abstract. We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to determine the coefficients of their perturbative expansions in the continuum limit. The method relies on identities satisfied by the resolvent of the Jacobi matrix in the three-term recursion relation of the associated families of orthogonal polynomials. These identities lead to a convenient formulation of the string equations. As an application, we show that in the continuum limit the free energy of certain exactly solvable models like the linear and double Penner models can be written as a sum of gaussian contributions plus linear terms. To illustrate the one-cut case we discuss the linear, double and cubic Penner models, and for the two-cut case we discuss theoretically and numerically the existence of a double-branch structure of the free energy for the gaussian Penner model.

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Section: The Z 2 -Symmetric Gaussian Penner Modelmentioning

confidence: 99%

“…and underlies many of the applications of these models in theoretical physics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. The partition functions of several Penner models can be explicitly calculated using Selberg's integral or some of its consequences [20], and turn out to be products and quotients of Euler's gamma functions.…”

Section: Introductionmentioning

confidence: 99%

Partition functions and the continuum limit in Penner matrix models

Álvarez¹,

Alonso²,

Медина³

2014

J. Phys. A: Math. Theor.

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“…Using the method discussed in [18,19], we get two sets of generating functions for even and odd polynomials. As each polynomial gives the generating function independent of the other, it is sufficient to work with either of the two polynomials (for a complete derivation, refer to [18,19]).…”

Section: Matrix Model Of Rna With Nonlinear External Interactionmentioning

confidence: 99%

“…As each polynomial gives the generating function independent of the other, it is sufficient to work with either of the two polynomials (for a complete derivation, refer to [18,19]). For even polynomials, the generating function is given by…”

Section: Matrix Model Of Rna With Nonlinear External Interactionmentioning

confidence: 99%

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Genus distribution and thermodynamics of a random matrix model of RNA with Penner interaction

Bhadola

Deo

2013

Phys. Rev. E

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The nonlinear Penner external interaction is introduced and studied in the random matrix model of homo RNA. A numerical technique is developed to study the partition function, and a general formula is obtained for all lengths. The genus distribution function for the system is obtained, plotted, and compared with the genus distribution for the real RNA structures found from the protein databank. The genus distribution shows that the nonlinear interaction favors the formation of low genus structures and matches the result for real RNA structures. The distribution of structure with temperature suggests that nonlinear interaction is biased toward the planar structures. The variation of chemical potential with temperature and interaction strength indicates the presence of additional molecules in the system other than the magnesium ions and possibly represents a phase transition. The specific heat has a bump and its derivatives shows a double-peak behavior at a particular temperature. On analyzing the specific heat and derivatives for each genus separately, the planar structure (genus zero) is shown to contribute the most to the bump and double peak. This observation in the nonlinear model is similar to that observed in the unfolding experiments on RNA.

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Deformed Cauchy random matrix ensembles and large N phase transitions

Russo

2020

J. High Energ. Phys.

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We study a new hermitian one-matrix model containing a logarithmic Penner’s type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the potential has an absolute minimum at the origin, but beyond a certain value of the coupling the potential develops a double well. For a higher critical value of the coupling, the system undergoes a large N third-order phase transition.

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Structure combinatorics and thermodynamics of a matrix model with Penner interaction inspired by interacting RNA

Cited by 11 publications

References 43 publications

Partition functions and the continuum limit in Penner matrix models

Partition functions and the continuum limit in Penner matrix models

Genus distribution and thermodynamics of a random matrix model of RNA with Penner interaction

Deformed Cauchy random matrix ensembles and large N phase transitions

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