The XXZ Heisenberg model on random surfaces |
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Authors: | J Ambjørn A Sedrakyan |
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Institution: | 1. The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen, Denmark;2. Yerevan Physics Institute, Br. Alikhanyan str. 2, Yerevan-36, Armenia;3. Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radbaud University Nijmegen, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands |
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Abstract: | We consider integrable models, or in general any model defined by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ 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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