A quantum phase transition (QPT) is defined as the qualitative change in the ground state of a system as a nonthermal external parameter (e.g. doping, pressure or magnetic field) is tuned.

While a QPT can only occur at zero-temperature, it has a strong effect on the phase diagram in its vicinity and can give rise to strong correlations.

 

I introduce the relativistic quantum O(N) model which describes quantum phase transitions such as the Mott insulator-superfluid transition in boson gases trapped in optical lattices or the paramagnetic-antiferromagnetic transition in magnets. I present results about the universal properties of the model in the vicinity of the transition, both thermodynamical and dynamical.