Chemistry Reference
In-Depth Information
CHAPTER 4
Computing Quantum Phase
Transitions
Thomas Vojta
Department of Physics, Missouri University of Science and
Technology, Rolla, Missouri
PREAMBLE: MOTIVATION AND HISTORY
A phase transition occurs when the thermodynamic properties of a mate-
rial display a singularity as a function of the external parameters. Imagine, for
instance, taking a piece of ice out of the freezer. Initially, its properties change
only slowly with increasing temperature, but at 0
C, a sudden and dramatic
change occurs. The thermal motion of the water molecules becomes so strong
that it destroys the crystal structure. The ice melts, and a new phase of water
forms, the liquid phase. At the phase transition temperature of 0
C the solid
(ice) and the liquid phases of water coexist. A finite amount of heat, the so-
called latent heat, is required to transform the ice into liquid water at 0
C.
Phase transitions involving latent heat are called first-order transitions.
Another well-known example of a phase transition is the ferromagnetic transi-
tion of iron. At room temperature, iron is ferromagnetic, i.e., it displays a
spontaneous magnetization. With rising temperature, the magnetization
decreases continuously due to thermal fluctuations of the spins. At the transi-
tion temperature (the so-called Curie point) of 770
C, the magnetization
vanishes, and iron is paramagnetic at higher temperatures. In contrast to the
previous example, there is no phase coexistence at the transition temperature;
the ferromagnetic and paramagnetic phases instead become indistinguishable.
