A major area of interest in condensed matter physics over the past decades has been the emergence of new states of matter from strongly correlated electron systems. A few limited examples would be the emergence of unconventional superconductivity in the high-T superconductors and heavy-fermion systems, the appearance of the skyrmion magnetic vortex state in MnSi and magnetically mediated superconductivity in UGe$2$. While detailed studies of many of the emergent phases have been made, there are still many gaps in understanding of the underlying states and mechanisms that allow them to form. This work aims to add to knowledge of the basic physics behind such states, and the changes within them as they are tuned to approach new phases.

The cubic perovskite material SrTiO$3$ has been studied for many decades and is well-documented to be an incipient ferroelectric, theorised to exist in the absence of any tuning in the proximity of a ferroelectric quantum critical point. This work presents the first high-precision dielectric measurements under hydrostatic pressure carried out on a quantum critical ferroelectric, leading to a full pressure-temperature phase diagram for SrTiO$3$. The influence of quantum critical fluctuations is seen to diminish as the system is tuned away from the quantum critical point and a novel low temperature phase is shown to be emergent from it.

The Néel Temperature of the two-dimensional antiferromagnet FePS$3$ was found to increase linearly with applied hydrostatic pressure. Evidence of an insulator-metal transition is also presented, and an unexplained upturn in the resistivity at low temperatures in the metallic phase.