The XXZ Heisenberg model on random surfaces

TY - JOUR

T1 - The XXZ Heisenberg model on random surfaces

AU - Ambjørn, Jan

AU - Sedrakyan, A.

PY - 2013/9/21

Y1 - 2013/9/21

N2 - We consider integrable models, or in general any model dened by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is dened 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.

AB - We consider integrable models, or in general any model dened by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is dened 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.

U2 - 10.1016/j.nuclphysb.2013.06.017

DO - 10.1016/j.nuclphysb.2013.06.017

M3 - Journal article

SN - 0550-3213

VL - 874

SP - 877

EP - 888

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -