Numerical Simulations of Quantum Phase Transitions

Lecture at StatPhys 19, Xiamen, China, August 1995.
A.P. Young
In this talk I will describe some examples of quantum phase transitions with disorder and explain in what ways these transitions differ from conventional phase transitions at finite temperature. It will be explained that the $\epsilon$-expansion does not work and so much of what we know has come from numerical simulations. A novel feature is the importance of Griffiths singularities'', which come from rare, strongly correlated, regions of the system. Some recent results on the quantum spin glass will be discussed in a little more detail