Solution of Potts-3 and Potts-∞ matrix models with the equations of motion method

@article{Bonnet1999SolutionOP,
  title={Solution of Potts-3 and Potts-∞ matrix models with the equations of motion method},
  author={G. Bonnet},
  journal={Physics Letters B},
  year={1999},
  volume={459},
  pages={575-581}
}
  • G. Bonnet
  • Published 8 April 1999
  • Physics
  • Physics Letters B
Abstract In this letter, we show how one can solve easily the Potts-3 + branching interactions and Potts-∞ matrix models, by the means of the equations of motion (loop equations). We give an algebraic equation for the resolvents of these models, and their scaling behaviour. This shows that the equations of motion can be a useful tool for solving such models. 
5 Citations
Boundary States of the Potts Model on Random Planar Maps
We revisit the 3-states Potts model on random planar triangulations as a Hermitian matrix model. As a novelty, we obtain an algebraic curve which encodes the partition function on the disc with both
Yang-Lee zeros of the two- and three-state Potts model defined on phi3 Feynman diagrams.
TLDR
For the Ising model, an argument based on a symmetry of the saddle point equations leads to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs.
Sums of Random Matrices and the Potts Model on Random Planar Maps
We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix
Random Matrices, Boundaries and Branes
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated
Planar maps and random partitions
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their

References

SHOWING 1-10 OF 20 REFERENCES
Combinatorial solution of the two-matrix model
Abstract We write down and solve a closed set of Schwinger-Dyson equations for the two-matrix model in the large N limit. Our elementary method yields exact solutions for correlation functions
Renormalization group approach to matrix models
Abstract Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge c ⩽ 1, or not understood. It would be useful to devise an approximate scheme which would be
The large N expansion in quantum field theory and statistical physics : from spin systems to 2-dimensional gravity
This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The
Simplicial Quantum Gravity and Random Lattices
Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action -
Daul hep-th/9502014
  • Daul hep-th/9502014
Nucl
  • Phys. B6166
  • 1999
Nucl. Phys
  • Nucl. Phys
  • 1999
Nucl
  • Phys. B487 [FS]
  • 1997
Phys
  • Lett. B 318 (1993) 63, Nucl. Phys. B434 (1995) 283-318, and Phys. Lett. B398
  • 1997
B410 (93) 377
  • J. Ambjorn, G. Thorleifsson, M. Wexler, Nucl. Phys
  • 1995
...
1
2
...