Quantum phase transitions in random spin systems

We report a systematic numerical study of quantum critical phenomena in random spin systems. At zero temperature, quantum phase transitions in these systems are caused by the interplay of quantum fluctuations and ordering interactions with built-in quenched randomness. As demonstrated in the one dimensional case, random quantum spin systems show unusual critical behavior as compared to classical systems. In this thesis two short range random exchange quantum spin systems in realistic dimensions are studied: a three-dimensional Ising spin glass and a two-dimensional random Ising ferromagnet, both placed in a transverse magnetic field. An Ising spin glass in a transverse field has been realized in LiHo{dollar}sb{lcub}x{rcub}{dollar}Y{dollar}sb{lcub}1-x{rcub}{dollar}F{dollar}sb4{dollar} compound and studied in experiments. Novel critical behavior were observed for the experimental system in the quantum regime.; By a quantum-classical mapping, the d-dimensional quantum spin problems we investigate are converted to (d + 1)-dimensional classical spin problems with correlated disorder. Monte Carlo simulations are performed on them and their critical properties are analyzed based on extensive simulation data. A finite size shape scaling scheme is devised to compute the dynamic exponent z, thus facilitating the anisotropic scaling calculation of other universal critical exponents. We find the scaling scenario is more consistent with conventional, rather than activated dynamic scaling as suggested for the corresponding one dimensional system. We also study the Griffiths singularities of magnetic susceptibilities on the disordered side of the quantum phase transition due to rare fluctuations in quantum spin glass. The singularities are found to be especially strong because of the enhancement of quantum relevance of randomness in random quantum ferromagnet is discussed by Harris criterion and an exponent inequality of Chayes et al. A real space anisotropic Migdal-Kadanoff renormalization procedure is carried out for the random quantum ferromagnet. We find that correlated randomness is more relevant than the uncorrelated randomness appropriate for thermal phase transitions in disordered systems. Crossover effects are found to be important in explaining the numerical results for the two-dimensional random quantum ferromagnet.