Quantum phase transitions in random spin systems

A number of condensed matter systems undergo a phase transition at zero temperature as some external parameter (such as pressure, magnetic field, or amount of dirt) is varied. Quantum effects are often crucial to the physics of this phenomenon hence the name "quantum phase transitions". This thesis is concerned with a study of such zero temperature phase transitions in the presence of static randomness (due to impurities or other frozen defects in the system). Experimentally accessible quantum phase transitions often occur in the presence of strong randomness, and are very poorly understood. Theoretically, the description of such phenomena involving competition between various kinds of potential energy of interactions, quantum effects, and randomness presents a challenging problem, where there are as yet few reliable techniques. This thesis studies simple quantum statistical models with randomness as a useful starting point to obtain insight into more complex, realistic systems. Progress is reported in understanding various simple but non-trivial models of random quantum magnetic systems in the vicinity of a quantum phase transition. The results show that the effects of randomness may be quite dramatic, and lead to a phenomenology that is strikingly different from that of pure systems.