Fermionic Quantum Spin Glass Transitions

This article reviews recent progress of the analytical theory of quantum spin glasses (QSG). Exact results for infinite range and one loop renormalisation group calculations for finite range models of either insulating or metallic type are presented. We describe characteristics of fermionic spin glass transitions and of fermionic correlations which are affected by these transitions and by spin glass order. Connections between tricritical thermal-- and $T=0$ QSG transitions are described. A general phase diagram with tricritical QSG transitions caused either by random chemical potential or by elastic electron scattering, and implying discontinuous $T=0$--transitions in weak and in strong filling regimes, is also derived.