Hermitian Matrix Model with Plaquette Interaction

Abstract

We study a hermitian $(n+1)$-matrix model with plaquette interaction, ${\sum }_{i=1}^{n}M{A}_{i}M{A}_i$. By means of a conformal transformation we rewrite the model as an $O(n)$ model on a random lattice with a non polynomial potential. This allows us to solve the model exactly. We investigate the critical properties of the plaquette model and find that for $n\in ]-2,2]$ the model belongs to the same universality class as the $O(n)$ model on a random lattice.

15 pages, no figures, two references added

References in corpus (7)

• Exact Solution of the O(n) Model on a Random Lattice
• More on the exact solution of the O(n) model on a random lattice and an investigation of the case |n|>2
• Meander, Folding and Arch Statistics
• Supersymmetric Matrix Models and the Meander Problem
• Square Gravity
• Generalized Hirota Equations in Models of 2D Quantum Gravity
• Bilinear Functional Equations in 2D Quantum Gravity

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• The Circular, Elliptic Three Spin String from the SU(3) Spin Chain
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• Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions
• An Iterative Solution of the Three-colour Problem on a Random Lattice
• Coloring Random Triangulations
• Rotational Symmetry Breaking in Multi-Matrix Models
• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
• Hamiltonian Cycles on a Random Three-coordinate Lattice
• Exact Meander Asymptotics: a Numerical Check
• Variational Master Field for Large-N Interacting Matrix Models - Free Random Variables on Trial
• The asymmetric ABAB matrix model
• Vertex Models on Feynman Diagrams
• On gonihedric loops and quantum gravity
• Phase transitions and random matrices
• Highly entangled spin chains and 2D quantum gravity