Ordering transitions and localisation properties of frustrated systems - Pickles, T (2009)
In this work we investigate themes related to many-body systems in which multiple ground states are accessible, a condition known as frustration. Frustration can arise in a number of contexts, and we consider the consequences of this situation with some examples from condensed-matter physics. In some magnetic materials interactions between spins are such that no single spin configuration provides a unique ground state. In the class of frustrated magnets where the number of ground states is extensive, thermal fluctuations are strong even at temperatures significantly below the interaction strength. At such temperatures spins are highly correlated, and small perturbations may have profound consequences. In this thesis we provide an example of this. By considering classical n-component spins with nearest-neigbour exchange on a frustrated octahedral lattice we show that – in the limit where exchange interactions are large – the system is in a disordered, correlated phase where correlations have the form of a dipole field. This is termed a Coulomb phase. From this phase we induce an ordering transition, lifting the degeneracy with weak, additional short-range interactions. By studying the transition in the solvable limit of n → ∞, we discover that the transition has identical thermodynamics to that of a magnetic system interacting through long-range, dipolar forces. Finally, we provide a more apposite characterisation of the transition, where the high-temperature side of the transition is described through the fluctuations of solenoidal fields, and the ordering corresponds to a condensation of these fields. In a separate part of the thesis, we investigate the influence of disorder on frustrated lattices. We study a two-dimensional tight-binding model with nearest-neighbour hopping and on-site disorder. Restricting the allowed states to being those from the low-lying manifold of ground states, the disorder feeds through to act as effective disorder in the hopping terms, which decay algebraically with distance. The quasi-long range nature of this effective hopping leads to a situation in which the resultant single-particle eigenstates are critical, and we probe their behaviour numerically with a transfer matrix calculation.