scholarly journals Determinant formulas for matrix model free energy

JETP Letters ◽  
2005 ◽  
Vol 82 (3) ◽  
pp. 101-104 ◽  
Author(s):  
D. Vasiliev
Keyword(s):  
Free Energy ◽  
Matrix Model ◽  
Model Free

Algebraic geometry and matrix models

2018 ◽  
Author(s):  
Noureddine El Karoui
Keyword(s):  
Free Energy ◽  
Algebraic Geometry ◽  
Matrix Models ◽  
Matrix Model ◽  
Moduli Spaces ◽  
Algebraic Curves ◽  
Loop Equation ◽  
Model Free ◽  
Moduli Spaces Of Curves ◽  
Symplectic Invariants

This article discusses the connection between the matrix models and algebraic geometry. In particular, it considers three specific applications of matrix models to algebraic geometry, namely: the Kontsevich matrix model that describes intersection indices on moduli spaces of curves with marked points; the Hermitian matrix model free energy at the leading expansion order as the prepotential of the Seiberg-Witten-Whitham-Krichever hierarchy; and the other orders of free energy and resolvent expansions as symplectic invariants and possibly amplitudes of open/closed strings. The article first describes the moduli space of algebraic curves and its parameterization via the Jenkins-Strebel differentials before analysing the relation between the so-called formal matrix models (solutions of the loop equation) and algebraic hierarchies of Dijkgraaf-Witten-Whitham-Krichever type. It also presents the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations, along with higher expansion terms and symplectic invariants.

A CRITICAL MATRIX MODEL AT c=1

1991 ◽  
Vol 06 (03) ◽  
pp. 259-270 ◽  
Author(s):  
JACQUES DISTLER ◽  
CUMRUN VAFA
Keyword(s):  
Free Energy ◽  
Euler Characteristic ◽  
Matrix Model ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Continuum Theory ◽  
Critical Limit ◽  
Logarithmic Corrections

By taking the critical limit of Penner’s matrix model we obtain a continuum theory whose free energy at genus-g is the Euler characteristic of moduli space of Riemann surfaces of genus-g. The exponents, and the appearance of logarithmic corrections suggest that we are dealing with a theory at c=1.

scholarly journals 1/N2 Correction to Free Energy in Hermitian Two-Matrix Model

2005 ◽  
Vol 71 (3) ◽  
pp. 199-207 ◽  
Author(s):  
B. Eynard ◽  
A. Kokotov ◽  
D. Korotkin
Keyword(s):  
Free Energy ◽  
Matrix Model

ON THE BEHAVIOR OF STATISTICAL SUM OF A MODEL WITH YANG–LEE SINGULARITY NEAR CRITICAL POINT

1992 ◽  
Vol 07 (01) ◽  
pp. 21-23 ◽  
Author(s):  
D. B. SAHAKYAN
Keyword(s):  
Free Energy ◽  
Critical Point ◽  
Matrix Model

An one-matrix model of singularities on the torus has been investigated. We calculate the value of discontinuity of free energy asymptotics which tends to an infinity number of lattice sites at the critical point.

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