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arXiv · 1407.0076

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

J. Ambjorn·Sh. Khachatryan·A. Sedrakyan
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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.

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J. Ambjorn, Sh. Khachatryan, A. Sedrakyan. 2014-06-30. A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces. https://doi.org/10.1103/physrevd.92.026002

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