A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces

Abstract

We consider a spin-s Heisenberg model coupled to two-dimensional quantum gravity. We quantize the model using the Feynman path integral, summing over all possible two-dimensional geometries and spin configurations. We regularize this path integral by starting with the R-matrices defining the spin-s Heisenberg model on a regular 2d Manhattan lattice. 2d quantum gravity is included by defining the R-matrices on random Manhattan lattices and summing over these, in the same way as one sums over 2d geometries using random triangulations in non-critical string theory. We formulate a random matrix model where the partition function reproduces the annealed average of the spin-s Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.

arXiv comment18 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1304.6903

References in corpus (22)

• 2D Gravity and Random Matrices
• Transfer Matrix Formalism for Two-Dimensional Quantum Gravity and Fractal Structures of Space-time
• Critical exponent for the quantum Hall transition
• Rational Theories of 2D Gravity from the Two-Matrix Model
• Scaling in quantum gravity
• Multicritical Phases of the O(n) Model on a Random Lattice
• Quantum Hall effect in a one-dimensional dynamical system
• Exact Solution of the Six-Vertex Model on a Random Lattice
• Operator Spectrum and Exact Exponents of the Fully Packed Loop Model
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect
• The six-vertex model on random lattices
• The quantum space-time of c=-2 gravity
• Quantum geometry of topological gravity
• Localization length index in a Chalker-Coddington model: a numerical study
• Edge Excitations of an Incompressible Fermionic Liquid in a Disorder Magnetic Field
• Fully Packed O(n=1) Model on Random Eulerian Triangulations
• On the theory of plateau-plateau transitions in Quantum Hall Effect
• Network Models: Action formulation
• Hamiltonian Cycles on Random Eulerian Triangulations
• Grassmann-Gaussian integrals and generalized star products
• The XXZ Heisenberg model on random surfaces

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