Q-states Potts model on a random planar lattice

Abstract

We propose a matrix-model derivation of the scaling exponents of the critical and tricritical q-states Potts model coupled to gravity on a sphere. In close analogy with the $O(n)$ model, we reduce the determination of the one-loop-to-vacuum expectation to the resolution of algebraic equations; and find the explicit scaling law for the case q=3.

12 pages, 1 PostScript figure, with epsf

Cited by in corpus (25)

• On the fractal structure of two-dimensional quantum gravity
• Critical Gaussian multiplicative chaos: Convergence of the derivative martingale
• Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model
• Counting colored planar maps: algebraicity results
• 2D Quantum Gravity, Matrix Models and Graph Combinatorics
• Geometrical Interpretation of the KPZ Exponents
• Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model
• Solvable Matrix Models
• Potts Models on Feynman Diagrams
• Spanning forests in regular planar maps
• Liouville Quantum Gravity and KPZ
• A geometric approach to free variable loop equations in discretized theories of 2D gravity
• Nesting statistics in the O(n) loop model on random planar maps
• Kosterlitz--Thouless Phase Transitions on Discretized Random Surfaces
• Introduction to Monte Carlo for Matrix Models
• Critical behaviour of loop models on causal triangulations
• FZZT Brane Relations in the Presence of Boundary Magnetic Fields
• Planar maps and random partitions
• Liouville Brownian motion at criticality
• Phase transitions and random matrices
• Bilinear Functional Equations in 2D Quantum Gravity
• Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for $0<c<1$
• Exact Spectral Dimension of the Random Surface
• Bootstrap Method in Theoretical Physics
• A characterization of the Tutte polynomial via combinatorial embeddings