Frustration and disorder: classical spin liquids and Floquet-Anderson insulators

In this thesis, the physics of two systems is investigated, both of which support unconventional phases of matter. We investigate a frustrated system which has a classical spin liquid regime in the paramagnetic phase. We also consider a periodically-driven, disordered system and explore nonequilibrium regimes. Both systems exhibit macroscopic behaviour which differs strongly from the behaviour in standard scenarios. First, the properties of frustrated magnets and related systems are discussed. We introduce three-dimensional generalisations of a well-studied two-dimensional frustrated system. These generalisations consist of coupled layers of two-dimensional triangular lattice Ising antiferromagnets. We study three stackings that have nearest-neighbour interactions: two frustrated stackings (abc and abab) and the unfrustrated stacking (aaa). We use a combination of methods, including numerics and analytics, to show that these generalisations exhibit a strongly correlated, highly fluctuating regime known as a classical spin liquid. We show this by investigating the structure factor and correlations directly and by describing a mapping to a continuum field theory that gives further clarity about the classical spin liquid regime using a renormalisation group analysis and consideration of low-lying excitations in these systems. Second, we study the response of a disordered system to a time-periodic driving potential. We start in the context of Mott's work on a.c. conductivity in Anderson insulators and move beyond this to study the Floquet (long-time) regimes beyond linear response. Using Landau-Zener physics, we construct a description of the various regimes which are possible. We also present the results of thorough numerical studies of these systems.