This thesis documents a theoretical investigation into quantum multicritical points (QMCPs), where a system near zero temperature is unstable towards two distinct ordered phases. We focus on quantum multicritical points in metallic systems, where the two ordered phases are both magnetic, but with different ordering wavevectors. This situation must be described by multiple dynamical exponents, which complicate the analysis.
By adapting Hertz-Millis theory, we build a model of a QMCP which we analyse using a renormalisation group approach. The regions of the phase diagram are identified, and the specific heat, thermal expansion and Grüneisen parameter are found in each region. The resistivity at finite temperatures above a QMCP is found by numerically solving the Boltzmann equation in the presence of disorder, and both ferro- and antiferromagnetic spin fluctuations. We believe our results explain the peculiar properties of the quantum critical compounds NbFe2 and Ta(Fe1-xVx)2, and we make predictions about properties of these systems which have not currently been measured.
We then investigate the related model of a metamagnetic quantum critical end-point and an antiferromagnetic quantum critical point in close proximity on the phase diagram. Using a self-consistently renormalised approach we identify the regions of the phase diagram, and the thermodynamic properties in each region. We highlight the experimentally measurable signatures of multicriticality in this model.