  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.

High Energy Physics - Theory;Statistical Mechanics