Quantum phase transitions in an ion trap

Summary form only given. Nonlinear collective and interacting spin models have long endured as tractable, nonlinear quantum models with wide ranging relevance. Such models have appeared in nuclear physics, laser physics, condensed matter physics and of course as a theoretical laboratory to investigate aspects of nonlinear field theories. In many cases however the match between model and experiment is only qualitative. I will show how some of these models may be directly simulated on a linear ion trap with individual ion addressing as in the quantum computation architecture.