Simulating Interesting Quantum Spin Models with Trapped Ions

I will review recent experiments from Chris Monroe's group in  University of Maryland, College Park, where they implement spin models like the Quantum Ising model with trapped ions. I will use a particular paper from the group, R. Islam et. al, Nature Communications, 2, 377 (2011), which studies "phase transitions" in ferromagnetic quantum Ising model, to detail how spin models can be implemented with trapped ions. Beyond this, I will also discuss how tunable long range interactions of both ferro and antiferromagnetic type can be generated with these systems. Finally, I will also discuss current plans to implement more interesting graphs of couplings in the physical 1D lattice to mimic 2D systems. 

References:
R. Islam et. al, Nature Communications 2, 377 (2011),
A. Sorensen and K Molmer, Phys. Rev. A 62, 022311 (2000)  ( Gives useful background, but couched in Quantum computation language)
S. Korenblit et. al, arXiv:1201.0776