If spin-ice materials had very strong quantum fluctuations, they would not be able to order as spin-ice at all; fluctuations would melt the system into a spin liquid.
But there is one recent reference that covers all of your questions: http://prx.aps.org/abstract/PRX/v1/i2/e021002
They report theory work (providing the model hamiltonian you asked for) and neutron scattering data to describe the strongly fluctuating rare-earth pyrochlore Yb$_2$Ti$_2$O$_7$.
In the context of the original question by PI-CMT, and in relation to the answer regarding Yb$_2$Ti$_2$O$_7$, one might find the following talk on the PI talk archive of some use: http://pirsa.org/index.php?p=speaker&name=Rajiv_R.P._Singh posted on June 15 2012.
This post imported from StackExchange Physics at 2014-04-05 16:30 (UCT), posted by SE-user wsc