The XXZ Heisenberg model on random surfaces

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.

15 pages

References in corpus (2)

• Large scale correlations in normal and general non-Hermitian matrix ensembles
• On the theory of plateau-plateau transitions in Quantum Hall Effect

Cited by in corpus (2)

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