Two-Matrix model with ABAB interaction

Abstract

Using recently developed methods of character expansions we solve exactly in the large N limit a new two-matrix model of hermitean matrices A and B with the action S={1\over 2}(\tr A^2+\tr B^2)-{α\over 4}(\tr A^4+\tr B^4) -{β\over 2} \tr(AB)^2. This model can be mapped onto a special case of the 8-vertex model on dynamical planar graphs. The solution is parametrized in terms of elliptic functions. A phase transition is found: the critical point is a conformal field theory with central charge c=1 coupled to 2D quantum gravity.

harvmac, 24 pages, 5 figures (1 color figure)

References in corpus (2)

• Universality of correlation functions of hermitian random matrices in an external field
• Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces

Cited by in corpus (26)

• Six-Vertex Model with Domain Wall Boundary Conditions and One-Matrix Model
• Complex Curve of the Two Matrix Model and its Tau-function
• Exact Solution of the Six-Vertex Model on a Random Lattice
• Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• The six-vertex model on random lattices
• Renormalization of 3d quantum gravity from matrix models
• Imposing causality on a matrix model
• Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model
• A Hexagon Model for 3D Lorentzian Quantum Cosmology
• 3d Lorentzian, Dynamically Triangulated Quantum Gravity
• Character expansion method for the first order asymptotics of a matrix integral
• Rotational Symmetry Breaking in Multi-Matrix Models
• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Hurwitz numbers from Feynman diagrams
• The asymmetric ABAB matrix model
• The F model on dynamical quadrangulations
• Exponents for Hamiltonian paths on random bicubic maps and KPZ
• Comment on "The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization"
• Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
• Computations in Large N Matrix Mechanics
• The generating function of planar Eulerian orientations
• A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions
• Tau functions of the UC hierarchy as partition functions of matrix models