Nonperturbative solution of the Ising model on a random surface
- 12 February 1990
- journal article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 64 (7), 717-720
- https://doi.org/10.1103/physrevlett.64.717
Abstract
The two-matrix-model representation of the Ising model on a random surface is solved exactly to all orders in the genus expansion. The partition function obeys a fourth-order nonlinear differential equation as a function of the string coupling constant. This equation differs from that derived for the k=3 multicritical one-matrix model, thus disproving that this model describes the Ising model. A similar equation is derived for the Yang-Lee edge singularity on a random surface, and is shown to agree with the k=3 multicritical one-matrix model.Keywords
This publication has 7 references indexed in Scilit:
- FRACTAL STRUCTURE OF 2d—QUANTUM GRAVITYModern Physics Letters A, 1988
- The ising model on a random planar lattice: The structure of the phase transition and the exact critical exponentsPhysics Letters B, 1987
- Ising model on a dynamical planar random lattice: Exact solutionPhysics Letters A, 1986
- Ising model of a randomly triangulated random surface as a definition of fermionic string theoryPhysics Letters B, 1986
- Conformal Invariance and the Yang-Lee Edge Singularity in Two DimensionsPhysical Review Letters, 1985
- A method of integration over matrix variablesCommunications in Mathematical Physics, 1981
- Statistical Theory of Equations of State and Phase Transitions. I. Theory of CondensationPhysical Review B, 1952